• Thumbnail for Uniform matroid
    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...
    7 KB (1,001 words) - 20:19, 1 April 2025
  • In combinatorics, a matroid /ˈmeɪtrɔɪd/ is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many...
    60 KB (8,774 words) - 11:35, 31 March 2025
  • Thumbnail for Matroid rank
    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...
    11 KB (1,426 words) - 09:36, 27 May 2025
  • Thumbnail for Graphic matroid
    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...
    16 KB (2,283 words) - 19:11, 1 April 2025
  • 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...
    14 KB (1,784 words) - 00:33, 9 November 2024
  • Thumbnail for Partition matroid
    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...
    7 KB (965 words) - 18:08, 30 April 2025
  • 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...
    3 KB (363 words) - 05:39, 29 January 2023
  • mathematics and computer science, a matroid oracle is a subroutine through which an algorithm may access a matroid, an abstract combinatorial structure...
    33 KB (4,287 words) - 21:15, 23 February 2025
  • Thumbnail for Free matroid
    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...
    3 KB (312 words) - 20:13, 1 April 2025
  • 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...
    8 KB (972 words) - 19:25, 1 April 2025
  • Thumbnail for Eulerian matroid
    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...
    8 KB (1,078 words) - 21:52, 1 April 2025
  • Thumbnail for Gammoid
    Gammoid (category Matroid theory)
    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...
    10 KB (1,453 words) - 18:27, 13 May 2025
  • 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...
    7 KB (851 words) - 07:14, 30 January 2023
  • a matroid polytope, also called a matroid basis polytope (or basis matroid polytope) to distinguish it from other polytopes derived from a matroid, is...
    8 KB (1,428 words) - 00:22, 9 November 2024
  • Thumbnail for Paving matroid
    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...
    7 KB (918 words) - 07:01, 11 November 2024
  • 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...
    16 KB (1,995 words) - 04:03, 25 September 2024
  • In the mathematics of matroids and lattices, a geometric lattice is a finite atomistic semimodular lattice, and a matroid lattice is an atomistic semimodular...
    8 KB (1,219 words) - 06:40, 9 May 2025
  • Hence, the concept of basis of a matroid generalizes the concept of basis from linear algebra. In a uniform matroid, where the independent sets are all...
    11 KB (1,639 words) - 06:34, 14 May 2025
  • 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...
    21 KB (2,835 words) - 22:59, 22 May 2025
  • 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...
    7 KB (825 words) - 00:12, 9 November 2024
  • Thumbnail for Branch-decomposition
    Branch-decomposition (category Matroid theory)
    is the uniform matroid U(2,3), the graphic matroid of the triangle graph. A matroid has branchwidth two if and only if it is the graphic matroid of a graph...
    21 KB (2,449 words) - 02:47, 16 March 2025
  • Thumbnail for K-set (geometry)
    K-set (geometry) (category Matroid theory)
    \lambda } the weight of the largest element in an optimal basis in a uniform matroid, and Dey showed that his O ( n k 1 / 3 ) {\displaystyle O(nk^{1/3})}...
    16 KB (1,881 words) - 05:33, 9 November 2024
  • downwards-closed non-matroid constraint. The approximation factors obtainable by an SPM are naturally better: Uniform matroid, partition matroid - e/(e-1) ≅ 1...
    18 KB (2,918 words) - 10:27, 9 December 2024
  • 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...
    24 KB (3,459 words) - 18:27, 22 May 2025
  • matroid. In the n {\displaystyle n} -point line (i.e., the rank 2 uniform matroid on n {\displaystyle n} elements, U n 2 {\displaystyle U{}_{n}^{2}}...
    4 KB (473 words) - 01:58, 23 December 2024
  • Zonohedron (category Oriented matroids)
    matrix whose columns are the v i {\displaystyle v_{i}} . Then the vector matroid M _ {\displaystyle {\underline {\mathcal {M}}}} on the columns of M {\displaystyle...
    25 KB (2,520 words) - 02:19, 8 December 2024
  • Thumbnail for Matroid parity problem
    combinatorial optimization, the matroid parity problem is a problem of finding the largest independent set of paired elements in a matroid. The problem was formulated...
    24 KB (3,443 words) - 01:40, 23 December 2024
  • Thumbnail for Discrete geometry
    Configurations Line arrangements Hyperplane arrangements Buildings An oriented matroid is a mathematical structure that abstracts the properties of directed graphs...
    15 KB (1,575 words) - 05:36, 16 October 2024
  • Thumbnail for Hypersimplex
    Hypersimplex (category Uniform polytopes)
    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...
    7 KB (599 words) - 10:13, 24 September 2024
  • Thumbnail for Cyclomatic number
    Cyclomatic number (category Matroid theory)
    dimension of the cycle space of a graph, in terms of matroid theory as the corank of a graphic matroid, and in terms of topology as one of the Betti numbers...
    14 KB (1,749 words) - 17:12, 27 May 2025