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 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...

fixed-parameter tractable for linear matroids when parameterized both by the matroid rank and the field size of a linear representation. The "girth" terminology generalizes...

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...

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...

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...

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

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

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...

linearly independent. Every matroid with a linear representation of this type may also be represented as an algebraic matroid, by choosing an indeterminate...

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

or involve matroids, polytopes, partially ordered sets, or finite geometries. On the algebraic side, besides group theory and representation theory, lattice...

nature or involve matroids, polytopes, partially ordered sets, or finite geometries. On the algebraic side, besides group and representation theory, lattice...

|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...

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

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...

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

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

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

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

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...

he proved the matroid intersection theorem, a very general combinatorial min-max theorem which, in modern terms, showed that the matroid intersection problem...

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

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

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

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

{\displaystyle (0,1,2)} . Filtration (mathematics) Flag manifold Grassmannian Matroid Kostrikin, Alexei I. and Manin, Yuri I. (1997). Linear Algebra and Geometry...

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