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15
105
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The relation between the closure and the contraction of a matroid M.

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#combinatorics #discrete-mathematics #graph-theory #matroids #algebraic-combinatorics
62
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Why every component of a loopless matroid is flat?

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#combinatorics #graph-theory #combinatorial-game-theory #matroids #algebraic-combinatorics
42
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The relation between contraction and deletion in a matroid.

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#combinatorics #discrete-mathematics #graph-theory #matroids #algebraic-combinatorics
86
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Determining all self-dual uniform matroids.

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#combinatorics #discrete-mathematics #graph-theory #matroids #algebraic-combinatorics
25
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How to prove that a matroid restricted to a subset is still a matroid

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#matroids
83
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prove that $M\big[ \frac{A_1}{A_2}\big] = M[A_1].$

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#linear-algebra #matrices #graph-theory #matroids #algebraic-combinatorics
117
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Show that no row of $A$ contains exactly one non-zero entry.

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#linear-algebra #graph-theory #matrix-rank #matroids #algebraic-combinatorics
82
Views

Finding an $\mathbb R$-representation for $M^*.$

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#linear-algebra #matrices #graph-theory #matroids #algebraic-combinatorics
119
Views

Largest number of disjoint subsets of certain cardinality in bipartite graph such that every vertex is matched

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#algorithms #bipartite-graphs #matching-theory #matroids
39
Views

How to show that an independence system whose maximally independent subsets have same cardinality is a matroid

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#matroids
120
Views

If $e \notin C,$ then $C$ is the union of circuits of $M/e$

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#combinatorics #graph-theory #matroids
61
Views

Why always the Crapo beta invariant value greater than or equal zero?

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#lattice-orders #combinatorial-geometry #algebraic-graph-theory #matroids #algebraic-combinatorics
81
Views

Proving that $ \beta(M) = \beta (M - e) + \beta (M /e).$

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#lattice-orders #combinatorial-proofs #algebraic-graph-theory #matroids #algebraic-combinatorics
35
Views

Let $A\subset B$ be flats of a matroid $M$ such that $r(A)=r(B)<\infty$. Then $A = B$.

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#combinatorics #algebraic-graph-theory #matroids #algebraic-combinatorics
55
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What is the definition of affine independence then?

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#linear-algebra #combinatorics #affine-geometry #matroids #algebraic-combinatorics

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