List questions from matroids

Published on 11 Oct 2023 - 7:44

60

Views

Why every component of a loopless matroid is flat?

Published on 14 Oct 2023 - 17:41

40

Views

The relation between contraction and deletion in a matroid.

Published on 14 Oct 2023 - 20:21

84

Views

Determining all self-dual uniform matroids.

Published on 15 Oct 2023 - 2:29

24

Views

How to prove that a matroid restricted to a subset is still a matroid

Published on 15 Oct 2023 - 14:43

82

Views

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

Published on 19 Oct 2023 - 23:06

115

Views

Show that no row of $A$ contains exactly one non-zero entry.

Published on 20 Oct 2023 - 12:09

80

Views

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

Published on 20 Oct 2023 - 23:40

118

Views

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

Published on 21 Oct 2023 - 9:25

38

Views

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

Published on 23 Oct 2023 - 10:44

119

Views

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

Published on 23 Oct 2023 - 22:18

59

Views

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

Published on 20 Nov 2023 - 1:54

79

Views

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

Published on 20 Nov 2023 - 3:32

33

Views

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

Published on 23 Nov 2023 - 15:36

53

Views

What is the definition of affine independence then?

Published on 24 Nov 2023 - 3:37

List Question

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

Why every component of a loopless matroid is flat?

The relation between contraction and deletion in a matroid.

Determining all self-dual uniform matroids.

How to prove that a matroid restricted to a subset is still a matroid

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

Show that no row of $A$ contains exactly one non-zero entry.

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

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

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

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

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

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

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

What is the definition of affine independence then?

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