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In combinatorics, a matroid /ˈmeɪtrɔɪd/ is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many...

An oriented matroid is a mathematical structure that abstracts the properties of directed graphs, vector arrangements over ordered fields, and hyperplane...

Matroid, Inc. is a computer vision company that offers a platform for creating computer vision models, called detectors, to search visual media for objects...

delta-matroid or Δ-matroid is a family of sets obeying an exchange axiom generalizing an axiom of matroids. A non-empty family of sets is a delta-matroid if...

combinatorial optimization, the matroid parity problem is a problem of finding the largest independent set of paired elements in a matroid, a structure that abstracts...

Matroid partitioning is a problem arising in the mathematical study of matroids and in the design and analysis of algorithms. Its goal is to partition...

theory of matroids, a matroid representation is a family of vectors whose linear independence relation is the same as that of a given matroid. Matroid representations...

In mathematics, a uniform matroid is a matroid in which the independent sets are exactly the sets containing at most r elements, for some fixed integer...

theory of matroids, the rank of a matroid is the maximum size of an independent set in the matroid. The rank of a subset S of elements of the matroid is, similarly...

In mathematics, a bipartite matroid is a matroid all of whose circuits have even size. A uniform matroid U n r {\displaystyle U{}_{n}^{r}} is bipartite...

In the mathematical theory of matroids, a graphic matroid (also called a cycle matroid or polygon matroid) is a matroid whose independent sets are the...

mathematical theory of matroids, a paving matroid is a matroid in which every circuit has size at least as large as the matroid's rank. In a matroid of rank r {\displaystyle...

the matroid intersection problem is to find a largest common independent set in two matroids over the same ground set. If the elements of the matroid are...

In mathematics, a basis of a matroid is a maximal independent set of the matroid—that is, an independent set that is not contained in any other independent...

matroid of M. Then Whitney's planarity criterion can be rephrased as stating that the dual matroid of a graphic matroid M is itself a graphic matroid...

mathematics and computer science, a matroid oracle is a subroutine through which an algorithm may access a matroid, an abstract combinatorial structure...

a matroid polytope, also called a matroid basis polytope (or basis matroid polytope) to distinguish it from other polytopes derived from a matroid, is...

In mathematics, an algebraic matroid is a matroid, a combinatorial structure, that expresses an abstraction of the relation of algebraic independence....

In mathematics, a colored matroid is a matroid whose elements are labeled from a set of colors, which can be any set that suits the purpose, for instance...

In matroid theory, a mathematical discipline, the girth of a matroid is the size of its smallest circuit or dependent set. The cogirth of a matroid is...

In the mathematics of structural rigidity, a rigidity matroid is a matroid that describes the number of degrees of freedom of an undirected graph with...

mathematics, Coxeter matroids are generalization of matroids depending on a choice of a Coxeter group W and a parabolic subgroup P. Ordinary matroids correspond...

In matroid theory, an Eulerian matroid is a matroid whose elements can be partitioned into a collection of disjoint circuits. In a uniform matroid U n...

matroid theory, a binary matroid is a matroid that can be represented over the finite field GF(2). That is, up to isomorphism, they are the matroids whose...

In matroid theory, the dual of a matroid M {\displaystyle M} is another matroid M ∗ {\displaystyle M^{\ast }} that has the same elements as M {\displaystyle...

In the mathematical subject of matroid theory, the bicircular matroid of a graph G is the matroid B(G) whose points are the edges of G and whose independent...

In the mathematics of matroids and lattices, a geometric lattice is a finite atomistic semimodular lattice, and a matroid lattice is an atomistic semimodular...

In combinatorics, a matroid embedding is a set system (F, E), where F is a collection of feasible sets, that satisfies the following properties. Accessibility...

In mathematics, a partition matroid or partitional matroid is a matroid that is a direct sum of uniform matroids. It is defined over a base set in which...

In mathematics, the Vámos matroid or Vámos cube is a matroid over a set of eight elements that cannot be represented as a matrix over any field. It is...

of matroids, a minor of a matroid M is another matroid N that is obtained from M by a sequence of restriction and contraction operations. Matroid minors...

In mathematics, a regular matroid is a matroid that can be represented over all fields. A matroid is defined to be a family of subsets of a finite set...

matroid is a matroid endowed with a function that assigns a weight to each element. Formally, let M = ( E , I ) {\displaystyle M=(E,I)} be a matroid,...

In matroid theory, a Sylvester matroid is a matroid in which every pair of elements belongs to a three-element circuit (a triangle) of the matroid. In...

In matroid theory, a field within mathematics, a gammoid is a certain kind of matroid, describing sets of vertices that can be reached by vertex-disjoint...

hypercube. Zonotopes are intimately connected to hyperplane arrangements and matroid theory. The Minkowski sum of a finite set of line segments in R d {\displaystyle...

} In matroid theory, two particularly important special classes of matroids are the wheel matroids and the whirl matroids, both derived from...

rank-3 oriented matroid. The points and lines of geometries defined using other number systems than the real numbers also form matroids, but not necessarily...

A sparsity matroid is a mathematical structure that captures how densely a multigraph is populated with edges. To unpack this a little, sparsity is a...

free matroid over a given ground-set E is the matroid in which the independent sets are all subsets of E. It is a special case of a uniform matroid; specifically...

accomplishments, including foundational work in the fields of graph theory and matroid theory. Tutte's research in the field of graph theory proved to be of remarkable...

and number of connected components, with immediate generalizations to matroids. It is also the most general graph invariant that can be defined by a...

Matroid-constrained number partitioning is a variant of the multiway number partitioning problem, in which the subsets in the partition should be independent...

Not only the structure but also enumerative properties belong to matroid theory. Matroid theory was introduced by Hassler Whitney and studied as a part...

define the same object. Examples of cryptomorphic definitions abound in matroid theory and others can be found elsewhere, e.g., in group theory the definition...

are two matroids associated with a signed graph, called the signed-graphic matroid (also called the frame matroid or sometimes bias matroid) and the...

mathematics, a base-orderable matroid is a matroid that has the following additional property, related to the bases of the matroid. For any two bases A {\displaystyle...

semilattice, there is an analogous matroid-like structure called a semimatroid, which is a generalization of a matroid (and has the same relationship to...

as a matroid, whose elements are the points of the configuration and whose nontrivial flats are the lines of the configuration. In this matroid, a set...

machine learning. He is adjunct professor at Stanford University, CEO of Matroid, and a founding team member at Databricks. His work focuses on machine...

Mathematical Association of America for his expository article An introduction to matroid theory. Due to his collaboration on a 1977 paper with the Hungarian mathematician...

Configurations Line arrangements Hyperplane arrangements Buildings An oriented matroid is a mathematical structure that abstracts the properties of directed graphs...

unified in matroid theory by the girth of a matroid, the size of the smallest dependent set in the matroid. For a graphic matroid, the matroid girth equals...

springs Tutte homotopy theorem, on the composition of generalized paths in matroids Hanani–Tutte theorem on the parity of edge crossings in graph drawings...

area of matroids. He found a polyhedral description for all spanning trees of a graph, and more generally for all independent sets of a matroid. Building...

vector. Matroid rank functions Let Ω = { e 1 , e 2 , … , e n } {\displaystyle \Omega =\{e_{1},e_{2},\dots ,e_{n}\}} be the ground set on which a matroid is...

elements, or a matroid constraint where the elements have a known matroid structure and we want to only accept an independent set of the matroid. Prophet inequalities...

unified in matroid theory by the girth of a matroid, the size of the smallest dependent set in the matroid. For a graphic matroid, the matroid girth equals...

{\displaystyle K[T]} . A matroid that can be generated in this way is called an algebraic matroid. No good characterization of algebraic matroids is known, but certain...

a greedoid is a type of set system. It arises from the notion of the matroid, which was originally introduced by Whitney in 1935 to study planar graphs...

an important graph invariant, and is closely related to invariants of matroids, topological spaces, and matrices. In random graphs, a frequently occurring...

sets of a matroid. For example, every bundle must contain at most k items, where k is a fixed integer (this corresponds to a uniform matroid). Or, the...

efficient graph algorithms. They may also be generalized from graphs to matroids. Several important classes of graphs may be characterized as the graphs...

Mathematics at Louisiana State University. He is known for his expertise in matroid theory and graph theory. Oxley did his undergraduate studies in Australia...

structure theory of matroids. Excluding the Fano plane as a matroid minor is necessary to characterize several important classes of matroids, such as regular...

transformation. For a matroid with n {\displaystyle n} elements and matroid rank r {\displaystyle r} , the corank or nullity of the matroid is n − r {\displaystyle...

paper, the term thagomizer graph (and also the associated "thagomizer matroid") was introduced for the complete tripartite graph K1,1,n. In 2023, researchers...

algebraic (or semialgebraic) varieties as realization spaces of oriented matroids. Informally it can also be understood as the statement that point configurations...

B is unbalanced. Biased graphs are interesting mostly because of their matroids, but also because of their connection with multiary quasigroups. See below...

Branch-decompositions and branchwidth may also be generalized from graphs to matroids. An unrooted binary tree is a connected undirected graph with no cycles...

Institute of Technology. His doctoral dissertation was titled, On Infinite Matroids, PhD in 1970 from Cornell University. Wagstaff was one of the founding...

matroid M {\displaystyle M} ; S {\displaystyle S} is said to be a representation of any matroid isomorphic to M {\displaystyle M} . Not every matroid...

planar if and only if its graphic matroid is also cographic (that is, it is the dual matroid of another graphic matroid). In purely graph-theoretic terms...

object. In a matroid, every subset of an independent set is again independent. This is a hereditary property of sets. A family of matroids may have a hereditary...

Coding theory, including error correcting codes and a part of cryptography Matroid theory Discrete geometry Discrete probability distributions Game theory...

matroid theory, the family of sets complementary to the independent sets of a given matroid themselves form another matroid, called the dual matroid....

analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex...

analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex...

by Jack Edmonds in 1970. It is also a generalization of the notion of a matroid. Let E {\displaystyle E} be a finite set and f : 2 E → R ≥ 0 {\displaystyle...

length of a shortest cycle contained in a graph Matroid girth, the size of the smallest circuit in a matroid Girth (album), 1997 album by heavy metal band...

analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex...

dimension of the cycle space of the graph, in terms of matroid theory as the dual rank of its graphic matroid, and in terms of topology as one of the Betti numbers...

analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex...

fact, they have at most as many edges as they have vertices) – and their matroid structure allows several other families of sparse graphs to be decomposed...

geometric lattices and matroids, this lattice of partitions of a finite set corresponds to a matroid in which the base set of the matroid consists of the atoms...

3-sums of graphic matroids (the matroids representing spanning trees in a graph), cographic matroids, and a certain 10-element matroid. Lovász (2006). As...

Thus the combinatorial topics may be enumerative in nature or involve matroids, polytopes, partially ordered sets, or finite geometries. On the algebraic...

and in full combinatorial pregeometry, are essentially synonyms for "matroid". They were introduced by Gian-Carlo Rota with the intention of providing...

In linear algebra and matroid theory, Rota's basis conjecture is an unproven conjecture concerning rearrangements of bases, named after Gian-Carlo Rota...

also active as a DJ. His research is in combinatorics, with a focus on matroid theory. Ardila is currently a professor at Queen Mary University of London...

(graph theory), a relation of one graph to another Minor (matroid theory), a relation of one matroid to another Minor (linear algebra), the determinant of...

algebras, Boolean algebras, distributive lattices, and geometric lattices (matroids). These lattice-like structures all admit order-theoretic as well as algebraic...

form the bases of a graphic matroid, so Kirchhoff's theorem provides a formula for the number of bases in a graphic matroid. The same method may also be...

node to itself Cycle graph, a graph that is itself a cycle Cycle matroid, a matroid derived from the cycle structure of a graph Cycle (sequence), a sequence...

to solve a class of linear combinatorial optimization problems with a matroid structure. Later Bernhard Korte and László Lovász characterized a broader...

semimodular bounded lattice is called a matroid lattice because such lattices are equivalent to (simple) matroids. An atomistic semimodular bounded lattice...

analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex...

special case of a more general matroid partitioning problem, in which one wishes to express a set of elements of a matroid as a union of a small number...

also be expressed using the theory of matroids, according to which a spanning tree is a base of the graphic matroid, a fundamental cycle is the unique circuit...

professor of Oxford University's Mathematical Institute. He was an expert in matroid theory, the computational complexity of combinatorial enumeration problems...

his contributions to optimization, polyhedral computation and oriented matroid theory. Fukuda is a professor in optimization and computational geometry...

optimization. He is known for his work on matroid theory and the extension of the Graph Minors Project to representable matroids. In 2003, he won the Fulkerson Prize...

to determine the existence of a transversal which is independent in a matroid. Hall 1986, pg. 51. An alternative form of the marriage theorem applies...

nodes, 68 different degree sequences of four-node connected graphs, and 68 matroids on four labeled elements. Størmer's theorem proves that, for every number...

pointy appearance in certain drawings) and their graphic matroids have been called thagomizer matroids. Triangular books form one of the key building blocks...

finite sets form the basis sets of a matroid, the transversal matroid of C. The independent sets of the transversal matroid are the partial transversals of...

Intersection of two partition matroids - 6.75 Intersection of a graphic matroid and a partition matroid - 10.66 General matroid with matroid rank k {\displaystyle...

S. R. Murty (1971) Equicardinal matroids. Journal of Combinatorial Theory, Series B U. S. R. Murty (1970) Matroids with Sylvester property. Aequationes...

In mathematical optimization, Cunningham's rule (also known as least recently considered rule or round-robin rule) is an algorithmic refinement of the...

(graph theory), a symmetric tessellation of a closed surface Regular matroid, a matroid which can be represented over any field Regular paperfolding sequence...

to Cornell in 1978. Bland is known as one of the inventors of oriented matroids, which he used to define Bland's rule for avoiding cycles in the simplex...

S and X to the case where X has a matroid structure and matchings must match to an independent set in the matroid on X. The Klarner–Rado Sequence is...

analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex...

flip graph. Each rank-3 oriented matroid is equivalent to an arrangement of pseudolines, and each oriented matroid which is also uniform (in which the...

configurations) appear in a characterization of the graphic matroids by forbidden matroid minors. Wagner, K. (1937), "Über eine Eigenschaft der ebenen...

the abstract setting of oriented matroids, Bland's rule cycles on some examples. A restricted class of oriented matroids on which Bland's rule avoids cycling...

on algebraic combinatorics, analytic combinatorics, graph theory, and matroid theory. Until December 2019, the journal was edited by George Andrews,...

set for the group Rank of a Lie group – see Cartan subgroup Rank of a matroid, the maximal size of an independent set Rank of a partition, at least two...

mathematical underpinnings related to the Brouwer fixed-point theorem, matroids and graph connectivity. Hex is a finite, two-player perfect information...

theorem. Paul Seymour for generalizing the max-flow min-cut theorem to matroids. 1982: D.B. Judin, Arkadi Nemirovski, Leonid Khachiyan, Martin Grötschel...

theory. He (with others) was responsible for important progress on regular matroids and totally unimodular matrices, the four colour theorem, linkless embeddings...

geometry. His work on matroids culminated in the paper "Representation of matroids" published in 1969. In his work, Ingleton studied matroids as a generalization...

was a Japanese mathematician who independently invented the theory of matroids, though his work was forgotten for many years. He published four papers...

for geometric lattices, the proof of the Heron–Rota–Welsh conjecture for matroids, the development of the theory of Lorentzian polynomials, and the proof...

Philippe Louis Jaeger was a French mathematician, working in graph theory, matroid theory, and knot theory. Jaeger was born in Boulogne-Billancourt to a father...

Bokowski, J.; Guedes de Oliveira, A. (2000), "On the generation of oriented matroids", Discrete and Computational Geometry, 24 (2–3): 197–208, doi:10.1007/s004540010027...

Heron–Rota–Welsh conjecture on the log-concavity of the characteristic polynomial of matroids. With Huh, he is one of five winners of the 2019 New Horizons Prize for...

(1972), Cheng and Liu (2007), and Gutman and Borovićanin (2011). In the matroid theory the nullity of the graph is the nullity of the oriented incidence...

and that this definition does agree with matrix rank as here discussed. Matroid rank Nonnegative rank (linear algebra) Rank (differential topology) Rank–nullity...

recognizing the generalization by Saunders Mac Lane of Steinitz's lemma to matroids. Let U {\displaystyle U} and W {\displaystyle W} be finite subsets of a...

analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex...

analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex...

the University of North Carolina, Chapel Hill. He worked primarily in matroid theory. Brylawski was born in 1944, and grew up in Washington, D.C. He...

Heron–Rota–Welsh conjecture on the log-concavity of the characteristic polynomial of matroids. With Joseph Rabinoff and David Zureick-Brown, he has given bounds on rational...

graph theory culminated in a 1933 paper where he laid the foundations for matroids, a fundamental notion in modern combinatorics and representation theory...

of bipartiteness to hypergraphs. Bipartite matroid, a class of matroids that includes the graphic matroids of bipartite graphs Bipartite network projection...

reduction can in fact be performed as the complex is constructed by using matroid theory, leading to further performance increases. Another recent algorithm...

Combinatorial Theory, Series B, 96(3), 388–404. Truemper, Klaus (1992), Matroid Decomposition (PDF), Academic Press, pp. 100–101, archived from the original...

(ビービネイル, Bībi Neiru) to enlarge the Matroids. Metal Alice is voiced by Marina Inoue (井上 麻里奈, Inoue Marina). The Matroids (マトロイド, Matoroido) are the Matrintis...

an infinite matroid, or pregeometry. A model of a strongly minimal theory is determined up to isomorphism by its dimension as a matroid. Totally categorical...

specializing in graph theory, including the interplay among graph minors, matroid theory, tree decomposition, and infinite graphs. He holds the chair of...

configuration. This matroid and its dual matroid have been applied in characterizing certain classes of matroids that are linear matroids over the finite...

set of vectors in a vector space. Independent set of elements of a matroid. See Matroid#Independent sets. Independent set (graph theory), a set of vertices...

Federico Ardila, a Colombian mathematician specializing in combinatorics and matroid theory. In 2019, Khoe joined Ardila on a sabbatical which involved traveling...

analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex...

graph is the nullity of its adjacency matrix, which equals n − r. In the matroid theory of graphs the rank of an undirected graph is defined as the number...

seminal. The rational singularity and fundamental cycles, which are used in matroid theory, are such examples of his sheer originality and thinking. He began...

(2009). A Lost Mathematician, Takeo Nakasawa: The Forgotten Father of Matroid Theory. Springer. p. 15. Hosie, Alexander (1910). Manchuria; its people...

on his previous papers on oriented-matroid theory. However, Bland's rule exhibits cycling on some oriented-matroid linear-programming problems. The first...

(2007). "On D.K. Biss' papers "The homotopy type of the matroid Grassmannian" and "Oriented matroids, complex manifolds, and a combinatorial model for BU""...

|V|=\max(|F|,\dim V).} A vector space can be seen as a particular case of a matroid, and in the latter there is a well-defined notion of dimension. The length...

other repeated vertices than the starting and ending vertices Circuit of a matroid Circuit (neural network), a computational subgraph within an artificial...

of Max-Flow Min-Cut Theorem". Combinatorial Optimization: Networks and Matroids. Dover. pp. 117–120. ISBN 0-486-41453-1. Lemaréchal, Claude (2001). "Lagrangian...

analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex...

the Shannon switching game played on a directed graph and an oriented matroid have been described for theoretical purposes; but no corresponding commercial...

rigidity of rod-and-hinge linkages is described by a matroid. The bases of the two-dimensional rigidity matroid (the minimally rigid graphs in the plane) are...

Coxeter matroids; it was published by Serganova and Israel Gelfand in 1987 as part of their research originating the concept of a Coxeter matroid. "Book...

can be generalized to one of parametric optimization in a matroid: one is given a matroid in which each element is weighted by a linear function of a...

bridgeless and almost-Eulerian), but they do not contain each other. Eulerian matroid, an abstract generalization of Eulerian graphs Five room puzzle Handshaking...

Title Role Episodes Tensou Sentai Goseiger Matroid Metal Alice of the Agent 33-44 Kaizoku Sentai Gokaiger Metal Alice of the Agent 40...

{\displaystyle G} . It can be computed in polynomial time as a special case of the matroid parity problem. The quantity τ ( G ) {\displaystyle \tau (G)} is the size...

of Mathematical Logic, University of Leeds Aubrey William Ingleton 1967 Matroids Fellow Robin Wilson 1962 graph theory Professor, Open University public...

Heron–Rota–Welsh conjecture on the log-concavity of the characteristic polynomial of matroids. With Karim Adiprasito, he is one of the five winners of the 2019 New Horizons...

Brigitte Irma Servatius (born 1954) is a mathematician specializing in matroids and structural rigidity. She is a professor of mathematics at Worcester...

shortest-path trees, flows and circulations, spanning trees, matching, and matroid problems. For NP-complete discrete optimization problems, current research...

analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal...

algebraic geometry; her research has also involved algebraic combinatorics, matroid theory, Hermitian matrices, and spectrahedra in convex optimization. She...

G} form the bases of a matroid. Cameron, P. J; Fon-Der-Flaass, D. G (1995-11-01). "Bases for permutation groups and matroids". European Journal of Combinatorics...

oriented matroids; in particular, the Folkman–Lawrence topological representation theorem is "one of the cornerstones of the theory of oriented matroids". In...

(sets of size 2), and their vertices (sets of size 1). In the context of matroids and greedoids, abstract simplicial complexes are also called independence...

minimums of finite collections of polynomials. Rota's basis conjecture: for matroids of rank n {\displaystyle n} with n {\displaystyle n} disjoint bases B i...

analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex...

random oracle). Black box group Turing reduction Interactive proof system Matroid oracle Demand oracle Padding oracle attack van Melkebeek 2003, Section...

analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex...

Schrijver, 1988, vol. 2; 2nd ed., 1993) Systems Analysis by Graphs and Matroids (Kazuo Murota, 1987, vol. 3) Greedoids (Bernhard Korte, László Lovász,...

Known for Coxeter element Coxeter functor Coxeter graph Coxeter group Coxeter matroid Coxeter notation Coxeter's loxodromic sequence of tangent circles Coxeter–Dynkin...

Nancy Ann Neudauer is an American mathematician specializing in matroid theory and known for her work in mathematical outreach in Africa and South America...

research student of Peter Vámos. His doctoral thesis was "Representations of Matroids". Fenton was a postdoctoral fellow in the mathematics department at University...

augmentation property or the independent set exchange property yields a matroid. The following expression summarizes the relations between the terms: HYPERGRAPHS...

A and {x}. A finitary closure operator with this property is called a matroid. The dimension of a vector space, or the transcendence degree of a field...

analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex...

(link). Lawler, E.L. (1976), Combinatorial Optimization: Networks and Matroids, Holt, Rinehart and Winston Eiselt, H. A.; Gendreau, Michel; Laporte, Gilbert...

surface on which the graph is embedded. In matroids, a non-separating circuit is a circuit of the matroid (that is, a minimal dependent set) such that...

transformation to a more general computational problem on matroids, the matroid parity problem for linear matroids. Beineke, Lowell W.; Wilson, Robin J. (2009), Topics...

its original position horizontally, vertically, or diagonally, and 185 matroids on five labeled elements in which each element participates in at least...

of choice is true. Thus the two assertions are equivalent. Basis of a matroid Basis of a linear program Coordinate system Change of basis – Coordinate...

Method of computing optimal strategies for last-success problems Oriented matroid – Abstraction of ordered linear algebra Quadratic programming – Solving...

(2014). "Polynomial-time T-count optimization of Clifford+T circuits via matroid partitioning". Proceedings of the 46th ACM Symposium on Theory of Computing...

the graphic matroid of a graph, a subset of edges is independent if the corresponding subgraph is a tree or forest. In the bicircular matroid, a subset...

Matroid aide Metal Alice arrive to use the Beebe Bugs they obtained to enlarge Zan-KT. After the Goseigers use Gosei Ultimate to destroy the Matroid,...

n-dimensional Euclidean space Flat (matroids), a further generalization of flats from linear algebra to the context of matroids Flat module in ring theory Flat...

and diversity. Topics in her research have included tropical geometry, matroid polytopes, Chow rings, toric varieties, lattices and semilattices, and...

definition of the span of points in space, a subset X of the ground set of a matroid is called a spanning set if the rank of X equals the rank of the entire...

His dissertation, Composition and Decomposition of Matroids and Related Topics, concerned matroid theory and was supervised by Louis Billera. His doctoral...

analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex...

(1983, p. 79) There are abstract optimization problems, called oriented matroid programs, on which Bland's rule cycles (incorrectly) while the criss-cross...

example Dihedral angle (between two planes). See also Angles between flats.) Matroid Coplanarity Isometry Gallier, J. (2011). "Basics of Affine Geometry". Geometric...

graph Nullity, the difference between the size and rank of a subset in a matroid Nullity, a concept in wheel theory denoted by ⊥, or similarly in transreal...

polyhedra, it is by now also capable of dealing with simplicial complexes, matroids, polyhedral fans, graphs, tropical objects, toric varieties and other objects...

applications of combinatorics. Series B is concerned primarily with graph and matroid theory. The two series are two of the leading journals in the field and...

LCPs can be solved when they are formulated abstractly using oriented-matroid theory. Complementarity theory Physics engine Impulse/constraint type physics...

mathematical structures other than graphs, and in particular in vector spaces and matroids. Two algorithmic problems are associated with MISs: finding a single MIS...

mean matrices that are invertible over the field. Balanced matrix Regular matroid Special linear group Total dual integrality Hermite normal form The term...

MR 2000133 Borovik, Alexandre V.; Gelfand, I. M.; White, Neil (2003), Coxeter matroids, Progress in Mathematics, vol. 216, Boston, MA: Birkhäuser Boston, ISBN 978-0-8176-3764-4...

Günter M. (1992), "Introduction to Greedoids", in White, Neil (ed.), Matroid Applications, Encyclopedia of Mathematics and its Applications, vol. 40...

optimization are: combinatorial optimization, which refers to problems on graphs, matroids and other discrete structures integer programming constraint programming...

Günter M. (1992), "Introduction to greedoids", in White, Neil (ed.), Matroid Applications, Encyclopedia of Mathematics and its Applications, vol. 40...

the pivot-minor relation are essentially equivalent to binary matroids with the matroid minor relation. For a circle graph G {\displaystyle G} , performing...

. Filtration (mathematics) Flag (geometry) Flag manifold Grassmannian Matroid Kostrikin, Alexei I. and Manin, Yuri I. (1997). Linear Algebra and Geometry...

1961. Elsevier. ISBN 9781483223568. Kazuo Murota (2009). Matrices and Matroids for Systems Analysis. Springer Science & Business Media. p. 47. ISBN 9783642039942...

in field extensions both form examples of finitary matroids (pregeometries). Any finitary matroid has a basis, and all bases have the same cardinality...

mathematics concerning the study of finite or countable discrete structures. Matroid Greedoid Ramsey theory Van der Waerden's theorem Hales–Jewett theorem Umbral...

education, and is known for his expertise in structural rigidity and rigidity matroids. Whiteley graduated from Queen's University in 1966. He earned his Ph.D...

finite semigroup theory. In recent years Rhodes brought semigroups into matroid theory. In 2015, he published, with Pedro V. Silva, the results of his...

of a relation is the smallest equivalence relation that contains it. In matroid theory, the closure of X is the largest superset of X that has the same...

may refer to The characteristic set of an algebraic matroid The characteristic set of a linear matroid Wu's method of characteristic set This disambiguation...

doi:10.1090/S0273-0979-1993-00335-5, MR 1164063. Truemper, Klaus (1992), Matroid Decomposition (PDF), Academic Press, pp. 100–101, archived from the original...

analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex...

Marc Roth: Counting restricted homomorphisms via Möbius inversion over matroid lattice 2016 Stefan Kratsch: A randomized polynomial kernelization for...

Michael; Sturmfels, Bernd; White, Neil; Ziegler, Günter M. (1999). Oriented Matroids (2nd ed.). Cambridge University Press. ISBN 0-521-77750-X. Björner, Anders;...

use it to describe separation in graphs. This usage has been extended to matroids. The balance of this article discusses Conway's sense of tangles; for the...

representable matroid. In this sense it is a necessary condition for representability of a matroid over a finite field. For a matroid M and its rank...

defining antimatroids as set systems are very similar to those of matroids, but whereas matroids are defined by an exchange axiom, antimatroids are defined instead...

G \ e denotes deletion. The numbers c, x, y, a, b are parameters. The matroid function f is TG if: f ( M 1 ⊕ M 2 ) = f ( M 1 ) f ( M 2 ) f ( M ) = a...

in any graph may be found in polynomial time using an algorithm for the matroid parity problem. Since triangular cactus graphs are planar graphs, the largest...

In mathematical optimization, Zadeh's rule (also known as the least-entered rule) is an algorithmic refinement of the simplex method for linear optimization...

networking) Flow graph (disambiguation) Max-flow min-cut theorem Oriented matroid Shortest path problem Nowhere-zero flow Active flow network A.V. Goldberg...

independent and M 1 + ⋯ + M d = X . {\displaystyle M_{1}+\cdots +M_{d}=X.} Matroid – Abstraction of linear independence of vectors G. E. Shilov, Linear Algebra...

polynomial time, by transforming it into an instance of the matroid parity problem for linear matroids. The special case of finding all feedback vertices in...

applications. CRC Press. ISBN 0-8493-3982-0. Oxley, James (2006) [1992]. Matroid Theory. Oxford University Press. ISBN 978-0-19-920250-8. Rosen, Kenneth...

cube, the Browder–Minty theorem, the introduction of oriented regular matroids, and the Minty-Vitaver theorem on graph coloring. George Minty Jr. grew...

author of the widely used textbook Combinatorial Optimization: Networks and Matroids and coauthor of The Traveling Salesman Problem: a guided tour of combinatorial...

Orthonormal basis Schauder basis Basis (universal algebra) Basis of a matroid Generating set of an ideal: Gröbner basis Hilbert's basis theorem Generating...

ISSN 0022-0000. Eugene Lawler (2001). "4. Network Flows". Combinatorial Optimization: Networks and Matroids. Dover. pp. 109–177. ISBN 978-0-486-41453-9....

the Witwatersrand, University of Cambridge, University of Waterloo Thesis Matroids on Complete Boolean Algebras  (1970) Doctoral advisor Gert Sabidussi...

Archived from the original on 2012-11-02. Retrieved 2009-04-26. Review of Matroids, motives, and a conjecture of Kontsevich MR 1950482 "Home page". Patrick...

Ardila, Federico; Klivans, Caroline J. (2006). "The Bergman complex of a matroid and phylogenetic trees". Journal of Combinatorial Theory, Series B. 96...

Sentai Shinkenger Ayakashi Yumebakura Ep. 25-26 2010 Tensou Sentai Goseiger Matroid Robogōgu of the 10-sai Eps. 33-43 2012 Tokumei Sentai Go-Busters Dumbbellloid...

combinatorial mathematics, a Dowling geometry, named after Thomas A. Dowling, is a matroid associated with a group. There is a Dowling geometry of each rank for each...

polynomial time, by transforming them into an instance of the matroid parity problem for linear matroids. Connected dominating sets are useful in the computation...

the bases of a matroid over the set of resources, then all best-response sequences converge in polynomial number of steps, and the matroid property is essential...

For example, 1.2E3 is 1.2×103 or 1200 the set of edges in a graph or matroid the unit prefix exa (1018) energy in physics electric field denoted E {\displaystyle...

convex hulls may also be generalized in a more abstract way, to oriented matroids. It is not obvious that the first definition makes sense: why should there...

hypersimplex Δ d , k {\displaystyle \Delta _{d,k}} is also the matroid polytope for a uniform matroid with d {\displaystyle d} elements and rank k {\displaystyle...

finds applications in error-correction codes, compressive sensing, and matroid theory, and provides a simple criterion for maximal sparsity of solutions...

analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex...

a set of points and lines without any two-point lines. Sylvester matroid, a matroid without any two-point lines. Sylvester's determinant identity. Sylvester's...

node for every clique of the underlying graph Partition matroid, a kind of matroid whose matroid intersections may form clique complexes Bandelt & Chepoi...

-graded sets. Signed sets are fundamental to the definition of oriented matroids. They may also be used to define the faces of a hypercube. If the hypercube...

of Max-Flow Min-Cut Theorem". Combinatorial Optimization: Networks and Matroids. Dover. pp. 117–120. ISBN 0-486-41453-1. Christos H. Papadimitriou, Kenneth...

research institutes in Canada and France. He is noted for his work in matroid theory and lattice theory. Crapo was born in Detroit, Michigan, in 1932...

Westermann, H. H. (1992), "Forests, frames, and games: algorithms for matroid sums and applications", Algorithmica, 7 (1): 465–497, doi:10.1007/BF01758774...

ISBN 978-0-521-59840-8, MR 1477750. Las Vergnas, Michel (1980), "Convexity in oriented matroids", Journal of Combinatorial Theory, Series B, 29 (2): 231–243, doi:10...

of a set in F {\displaystyle F} is also in ⁠ F {\displaystyle F} ⁠. A matroid is an abstract simplicial complex with an additional property called the...

a bit-length which is not polynomial in this representation. Oriented matroid Nef polyhedron Steinitz's theorem for convex polyhedra Branko Grünbaum...

2017-04-17 Lindström, Bernt (1973), On the vector representations of induced matroids, doi:10.1112/blms/5.1.85 Sagan, Bruce E. (2001), The symmetric group, Springer...

extension complexity. On the other hand, the independence polytope of regular matroids has polynomial extension complexity. The notion of extension complexity...

or a base of this matroid. Cardinality constraints are special cases of matroid constraints in which the matroid is a uniform matroid. Categorized cardinality...

M. (1992), "8. Introduction to greedoids" (PDF), in White, Neil (ed.), Matroid Applications, Encyclopedia of Mathematics and its Applications, vol. 40...

network with gains, or generalized network, is connected with the frame matroid of the gain graph. Suppose we have some hyperplanes in R n given by equations...

they allow for higher-dimensional simplices. Every graph gives rise to a matroid. In model theory, a graph is just a structure. But in that case, there...

 125–136. Ramirez Alfonsin, J. L. (1999), "Spatial graphs and oriented matroids: the trefoil", Discrete and Computational Geometry, 22 (1): 149–158, doi:10...

theory, in the process establishing connections between that field and matroid theory. Freiling obtained his Ph.D. in 1981 from the University of California...

Frequency partition Graph partition Kernel of a function Lamination (topology) Matroid partitioning Multipartition Multiplicative partition Noncrossing partition...

also known as the Euler integral of the first kind Beta invariant, of a matroid Dirichlet beta function Eratosthenes, Greek mathematician nicknamed Beta...

subset problem was studied with additional constraint represented by a matroid. Envy-free item allocation Participatory budgeting algorithm Multiwinner...

(2009). A Lost Mathematician, Takeo Nakasawa: The Forgotten Father of Matroid Theory. Springer. p. 15. Philippe Forêt (January 2000). Mapping Chengde:...

Mathematical Society. ISBN 978-3-03719-017-3. Kazuo Murota (2009). Matrices and Matroids for Systems Analysis. Springer Science & Business Media. ISBN 978-3-642-03994-2...

pregeometry has several meanings: Pregeometry (model theory), another name for a matroid Pregeometry (physics), a structure from which geometry arises This disambiguation...

rigid graphs, and they form the bases of the two-dimensional rigidity matroids. If n points in the plane are given, then there are 2n degrees of freedom...

the two configurations, including the fact that both are self-dual under Matroid duality. In abstract terms, the latter configuration has "points" 0, ....

"Cocircuit Graphs and Efficient Orientation Reconstruction in Oriented Matroids". Eur. J. Comb. 22 (5): 587–600. doi:10.1006/eujc.2001.0481. ISSN 0195-6698...

Rothvoss and Zhang improved the approximation factor to 4 by introducing matroid constraints to the basic linear program. For the general case, for agents...

the Bron–Kerbosch algorithm Listing all elements of structures such as matroids and greedoids Several problems on graphs, e.g., enumerating independent...

ISBN 9780262032933. Lawler, Eugene L. (2001), Combinatorial Optimization: Networks and Matroids, Courier Dover Publications, p. 64, ISBN 9780486414539. Sedgewick, Robert;...

affine Gale diagrams can also be described through the duality of oriented matroids. As with the linear diagram, a subset of vertices forms a face if and only...

1090/s0002-9939-1969-0236029-9. MR 0236029. Brualdi, Richard A. (1971). "Induced matroids". Proc. Amer. Math. Soc. 29 (2): 213–221. doi:10.1090/s0002-9939-1971-0289335-5...

for constraint satisfaction problems, and width parameters in graphs and matroids. She is an associate professor at KAIST. Kim studied industrial engineering...

Tutte) has "had a huge impact," in part because of its implications in matroid theory. Nash-Williams also studied k-edge-connected graphs, Hamiltonian...

mathematician specializing in disease modeling Collette Coullard, American matroid theorist and operations researcher Judith Covington, American mathematics...

American mathematician, industrial engineer, operations researcher, and matroid theorist known for her research on combinatorial optimization problems...

independently published on the criss-cross algorithm. The theory of oriented matroids has also been used by Terlaky and Zhang (1991) to prove that their criss-cross...

"The multivariate Tutte polynomial (alias Potts model) for graphs and matroids". Surveys in Combinatorics 2005. pp. 173–226. arXiv:math/0503607. doi:10...

geometry has been founded, having close connection, for example, with matroid theory. Synthetic differential geometry is an application of topos theory...

conjecture is still open. Matroid bundles. In 2003 Daniel Biss published a paper in the Annals of Mathematics claiming to show that matroid bundles are equivalent...

Specht module may be found in Section 1 of "Specht Polytopes and Specht Matroids". The dimension of the Specht module V λ {\displaystyle V_{\lambda }} is...

in any graph may be found in polynomial time using an algorithm for the matroid parity problem. Since triangular cactus graphs are planar graphs, the largest...

facets are available. Abstract polytope Combinatorial commutative algebra Matroid polytope Order polytope Simplicial sphere Stable matching polytope Ziegler...

N. Gabow and R.E. Tarjan, Journal of the ACM 38, 4, 1991, 815-853. "A matroid approach to finding edge connectivity and packing arborescences," H.N....

Bokowski, J.; Guedes de Oliveira, A. (2000), "On the Generation of Oriented Matroids", Discrete & Computational Geometry, 24: 197–208, doi:10.1007/s004540010027...

3247570. S2CID 248986512. Kühne, L.; Yashfe, G. (2022). "Representability of Matroids by c-Arrangements is Undecidable". Israel Journal of Mathematics. 252:...

Michel; Sturmfels, Bernd; White, Neil; Ziegler, Günter (1999), Oriented matroids, Encyclopedia of Mathematics and Its Applications, vol. 46 (2nd ed.), Cambridge...

characteristic polynomial, making it a graph determined by its spectrum. Vámos matroid Weisstein, Eric W. "Diamond Graph". MathWorld. ISGCI: Information System...

relation. This is equivalent to the definition of algebraic dependence. matroid This article incorporates material from Dependence relation on PlanetMath...

algebraic combinatorics, including work on cell complexes associated with matroids and on chip-firing games. She is an associate professor of applied mathematics...

factor-criticality has been extended to matroids by defining a type of ear decomposition on matroids and defining a matroid to be factor-critical if it has an...

introduced by Tutte (1958), generalises the concept of "path" from graphs to matroids, and states roughly that closed paths can be written as compositions of...

schemes defined by Kirchhoff polynomials to the representation spaces of matroids. Moreover, using Mnev's universality theorem, we show that these schemes...

problems that includes as special cases the minimum-cost flow problem, matroid intersection, and the problem of computing a minimum-weight dijoin in a...

is t-dependent; the t-dependent families form the dependent sets of a matroid, which Deza and his co-authors investigate. Deza, M.; Laurent, M. (1992)...

can be covered by edge-disjoint subgraphs. Arboricity Bridge (cut edge) Matroid partitioning Menger's theorem Tree packing conjecture Tutte, W. T. (1961)...

Beginning in 1975, he became one of the pioneers of the theory of oriented matroids, and since that time he was interested in connections between combinatorics...

Berkeley Max Planck Institute for Mathematics in the Sciences Thesis Oriented Matroids and Combinatorial Convex Geometry; Computational Synthetic Geometry Doctoral...

In the mathematical theory of functional analysis, the Krein–Milman theorem is a proposition about compact convex sets in locally convex topological vector...

Missouri. Her research interests include combinatorics, graph theory, and matroids. Carolyn Mahoney was born the sixth of thirteen children in 1946 in Memphis...

matroids. In this context, the core of a convex cost game is called the base polyhedron, because its elements generalize base properties of matroids....

Rider Decade (2009) – Garulu (ep. 4 - 5) Tensou Sentai Goseiger (2010) – Matroid Zuteru-S of the Mach (ep. 35) Kamen Rider × Kamen Rider Fourze & OOO: Movie...

S2CID 121878844 Golumbic, Martin Charles (1977), "Comparability graphs and a new matroid", Journal of Combinatorial Theory, Series B, 22 (1): 68–90, doi:10...

Section 4.3 Aharoni, Ron; Berger, Eli (2006). "The intersection of a matroid and a simplicial complex". Transactions of the American Mathematical Society...

analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex...

mathematics at Binghamton University since 1985. He has published papers on matroid theory and hyperplane arrangements. He has also written on coding theory...

important contributions in diverse areas of discrete mathematics, including matroid theory, matching theory, the max-cut and stable set problems, spectral...

e. is prime and minimal over) a strongly minimal set, which carries a matroid structure determined by (model-theoretic) algebraic closure that gives...

A. Harvey (MIT) "Algebraic Structures and Algorithms for Matching and Matroid Problems" 2005 Mark Braverman (Toronto) "On the Complexity of Real Functions"...

finite obstruction set. Erdős–Hajnal conjecture Forbidden subgraph problem Matroid minor Zarankiewicz problem Diestel, Reinhard (2000), Graph Theory, Graduate...

planarity criterion that a graph is planar if and only if its graphic matroid is also cographic, Mac Lane's planarity criterion characterizing planar...

featured the antagonistic robot group Matrintis. Their foot soldiers, the Matroids, followed perverted versions of the "Three Laws of Robotics": conquer humans...

Shinkenger: Kusare Ayakashi Azemidoro (ep. 31) Tensou Sentai Goseiger: Matroid Bakutofuji-ER of the Timer (ep. 39–40) Tokumei Sentai Go-Busters: Omochiloid...

Mathematisch für fortgeschrittene Anfänger : Weitere beliebte Beiträge von Matroids Matheplanet (in German). Heidelberg: Spektrum Akademischer Verlag. pp. 273–276...

Westermann, Herbert H. (1992), "Forests, frames, and games: algorithms for matroid sums and applications", Algorithmica, 7 (5–6): 465–497, doi:10.1007/BF01758774...

Zan-KT0 of the Shot (ショットのザンKT0, Shotto no Zan Kē Tī Zero): A scallop-themed Matroid and servant of the Matrintis Empire. He is deployed to destroy the Negakure...

Hall, Rhiannon; Oxley, James; Semple, Charles; Whittle, Geoff (2002). "On matroids of branch-width three". Journal of Combinatorial Theory, Series B. 86 (1):...

have smaller weight. By standard properties of bases in vector spaces and matroids, the minimum weight cycle basis not only minimizes the sum of the weights...

190. Lawler, Eugene L. (2001), Combinatorial optimization: networks and matroids, Dover Publications, pp. 222–223, ISBN 978-0-486-41453-9. "Prove that the...

MR 1964792, S2CID 34821155. Las Vergnas, Michel (1980), "Convexity in oriented matroids", Journal of Combinatorial Theory, Series B, 29 (2): 231–243, doi:10...

Transversals is an undergraduate-level mathematics textbook on the theory of matroids. It was written by Victor Bryant and Hazel Perfect, and published in 1980...

framework of separoids; e.g., graphs, configurations of convex sets, oriented matroids, and polytopes. Any countable category is an induced subcategory of separoids...

analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex...

(2003), Combinatorial optimization: Polyhedra and efficiency, Vol. B: Matroids, trees, stable sets, Algorithms and Combinatorics, vol. 24, Berlin: Springer-Verlag...

Lincoln University of Missouri Researched combinatorics, graph theory, and matroids Shirley M. Malcom zoologist 1946- Senior Advisor and Director of SEA Change...

equipped with a further oracle for determining element orders. Implicit graph Matroid oracle Babai, L.; Szemeredi, E. (1984). "On the Complexity of Matrix Group...

graph H. Graph minors are often studied in the more general context of matroid minors. In this context, it is common to assume that all graphs are connected...

first to recognize the importance of transversal matroids, and he showed that transversal matroids can be represented using linear algebra over transcendental...

of it include enumerative combinatorics, combinatorial design theory, matroid theory, extremal combinatorics and algebraic combinatorics, as well as...

"Fractional Arboricity Strength and Principal Partitions in Graphs and Matroids". Discrete Applied Mathematics. 40 (3): 285–302. doi:10.1016/0166-218X(92)90002-R...

surfaces) Richard Rado's theorem (Ramsey theory) Richard Rado's theorem (matroid theory) This disambiguation page lists mathematics articles associated...

public goods, with possible constraints on the allocation. They consider matroid constraints, matching constraints, and packing constraints (which correspond...

(2018). "Multiple exchange property for M♮-concave functions and valuated matroids". Mathematics of Operations Research. 43 (3): 781–788. arXiv:1608.07021...

abstract simplicial complex with the augmentation property is called a matroid. Laminar: for any two hyperedges, either they are disjoint, or one is included...

analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex...

Shinkenger (2009) (Ayakashi Sasamatage (ep. 20)) Tensou Sentai Goseiger (2010) (Matroid Adoborute-G of the Vital (ep. 37)) Albino Alligator (Milo (Gary Sinise))...

supersolvable, although it is not geometric. The lattice of flats of the graphic matroid for a graph is supersolvable if and only if the graph is chordal. Working...

York, 1994 Borovik, Alexandre V.; Gelfand, I. M.; White, Neil: Coxeter matroids. Progress in Mathematics, 216. Birkhäuser Boston, Inc., Boston, MA, 2003...

"The multivariate Tutte polynomial (Alias Potts model) for graphs and matroids". Surveys in Combinatorics 2005. pp. 173–226. arXiv:math/0503607. doi:10...

Victoria University of Wellington The mathematics of space and language: matroids and model theory Robert McKay Victoria University of Wellington Antarctic...

D. thesis, University of California, Berkeley. Truemper, Klaus (1992), Matroid Decomposition (PDF), Academic Press, pp. 100–101, archived from the original...

Stanley has had a big impact in contemporary combinatorics for his work in matroid theory, for introducing Zeta polynomials, for explicitly defining Eulerian...

analysis Measure theory Discrete Combinatorics Discrete geometry Graph theory Matroid theory Order theory Geometry Algebraic Affine Analytic Arithmetic Complex...

Elad; Carmesin, Johannes; Fröhlich, Jan-Oliver (2012-07-09), Infinite matroid union, arXiv:1111.0602 Blossier, Thomas; Bouscaren, Elisabeth (2010). "Finitely...

 147, American Mathematical Society, pp. 125–136. Truemper, Klaus (1992), Matroid Decomposition (PDF), Academic Press, pp. 100–101, archived from the original...

Thomas; Zhang, Yihao (2019-12-23), "A Tale of Santa Claus, Hypergraphs and Matroids", Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms, Proceedings...

satisfying the second condition form the independent sets of a sparsity matroid, and are called ( 2 , 3 ) {\displaystyle (2,3)} -sparse. A graph satisfying...

Munagala and Shah focus on three types of constraints: Matroid constraints: there is a fixed matroid M over the items, and the chosen items must form a basis...

used by German armed forces during World War II, leading contributor to matroid and graph theory; as William Thomas Tutte, in Newmarket, Suffolk, England...

3247570. S2CID 248986512. Kühne, L.; Yashfe, G. (2022). "Representability of Matroids by c-Arrangements is Undecidable". Israel Journal of Mathematics. 252:...

group, an implicit model for group-theoretic algorithms Matroid oracle, an implicit model for matroid algorithms Korf, Richard E. (2008), "Linear-time disk-based...

algorithms. 2018: Stefan Kratsch and Magnus Wahlström for their work using matroid theory to develop polynomial-size kernels for odd cycle transversal and...

University in 1975, with the dissertation Comparability Graphs and a New Matroid supervised by Samuel Eilenberg. He became an assistant professor in the...

concepts in structural (combinatorial) rigidity theory, such as the rigidity matroid. The following results concern the l p p {\displaystyle l_{p}^{p}} -distance...

In geometry, a zonohedron is a convex polyhedron that is centrally symmetric, every face of which is a polygon that is centrally symmetric (a zonogon)...

of Alaska Anchorage. Her research is in combinatorics, specializing in matroid theory and graph theory. McNulty majored in both chemistry and mathematics...

requirement that the union of all allocated goods is a basis of a given matroid. They used an algorithm similar to the envy-graph procedure. Suksompong...

Alexander; Krummeck, Vanessa; Richter-Gebert, Jurgen (2003). "Complex matroids: phirotopes and their realizations in rank 2". In Aronov, Boris; Basu,...

Michel; Sturmfels, Bernd; White, Neil; Ziegler, Günter M. (1993), Oriented Matroids, Encyclopedia of Mathematics and its Applications, vol. 46, Cambridge:...

several ways of constructing such graphs. Hobbs had also done research in matroid theory. Dr. Hobbs has 40 publications in graph theory, and in 1989 co-authored...

to the Grassmannian, neighbor joining in the space of metric trees, and matroids. Chapter five considers tropical analogues of some of the important concepts...

non-crossing spanning trees of planar point sets, and more generally bases of matroids, using a state space that swaps one edge for another. Euler tours in graphs...

the LYM inequality) Lucas chain MacMahon's master theorem Magic square Matroid embedding Monge array Monomial order Moreau's necklace-counting function...

correspondence between CC systems and uniform acyclic oriented matroids of rank 3. These matroids in turn have a 1-1 correspondence to topological equivalence...

in 2006. Her dissertation was supervised by T. James Reid and concerned matroid theory. She was the second African-American woman to earn a doctorate in...

"Exponentially many hypohamiltonian graphs", Graphs, Hypergraphs and Matroids III (Proc. Conf. Kalsk 1988), Zielona Góra: Higher College of Engineering...

operator (Cyclic decomposition of maximal monotone operator) Oriented matroids (realizable OMs and applications) Carathéodory's theorem (convex hull)...

Born: Takeo Nakasawa, Japanese mathematician, conceived the theory of matroid. His work was largely forgotten and would be rediscovered more than 60...

of disjoint cycles. Cycle basis Cycle double cover conjecture Eulerian matroid Sabidussi 1964. Euler, L. (1736), "Solutio problematis ad geometriam situs...

guarantee, that works for the more general problem of allocating a basis of a matroid. Li, Moulin, Sun and Zhou have extended Hill's lower bound to bads, and...

"type II" quasisymmetric power sums, and bases related to enumeration in matroids. Quasisymmetric functions have been applied in enumerative combinatorics...

the study of arrangements of pseudolines and (more generally) oriented matroids. His work with Pollack includes such results as the first nontrivial bounds...

Sylvester–Gallai designs. A closely related concept is a Sylvester matroid, a matroid with the same property as a Sylvester–Gallai configuration of having...

personal attendant, a Matrintis Empire marshal, and the first high-spec Matroid built by her master to serve him. Prior to her and Robogorg's battle with...

incidence matrices, submodular set functions, independent matchings in matroids, the Birkhoff–von Neumann theorem on the Birkhoff polytope of doubly stochastic...

The Avis–Fukuda algorithm adapted the criss-cross algorithm for oriented matroids. A 2025 article by Zelin Dong, Fenglei Fan, Huan Xiong, and Tieyong Zeng...

1007/978-3-319-44914-2_9. In P: Seymour, P. D. (June 1980). "Decomposition of regular matroids" (PDF). Journal of Combinatorial Theory, Series B. 28 (3): 305–359. doi:10...

Goemans, Michel; Olver, Neil; Rothvoss, Thomas; Zenklusen, Rico (2012). "Matroids and integrality gaps for hypergraphic steiner tree relaxations". Proceedings...

In mathematics, a supersolvable arrangement is a hyperplane arrangement that has a maximal flag consisting of modular elements. Equivalently, the intersection...

variant is known as the agreeable subset problem. There may be general matroid constraints, matching constraints or knapsack constraints on the chosen...

and using the Biswas-Barman algorithm for fair allocation with partition matroid constraints, or simply by round-robin item allocation. This guarantees...

Michel; Sturmfels, Bernd; White, Neil; Ziegler, Günter (1999), Oriented Matroids, Encyclopedia of Mathematics and Its Applications, vol. 46 (2nd ed.), Cambridge...

June 2020). Carolina Benedetti, Quotients of positroids and lattice path matroids, AlCoVE 2020. Retrieved 16 July 2025 – via YouTube. Quiceno, Juan Diego...

(2012), no. 4, 911–922. 2013 Branch decomposition heuristics for linear matroids Archived October 15, 2018, at the Wayback Machine (with Jing Ma, Susan...

1112/blms/18.6.571, MR 0859948 Ramírez Alfonsín, J. L. (2001), "Lawrence oriented matroids and a problem of McMullen on projective equivalences of polytopes", European...

fuzzy measures, fuzzy topological games, fuzzy commutative algebra, fuzzy matroids, etc. During the 79th Annual Conference of the Indian Mathematical Society...

supply constraints given as an independence system over the items, such as matroid constraints. They focus on unit-demand buyers. Chen and Deng study multi-item...