List questions from algebraic-combinatorics

Published on 13 Nov 2023 - 9:09

59

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

Published on 20 Nov 2023 - 1:54

79

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

Published on 20 Nov 2023 - 3:32

128

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Taylor Expansion of the Polynomial in Flajolet’s Fundamental Lemma

Published on 21 Nov 2023 - 2:28

33

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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

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What is the definition of affine independence then?

Published on 24 Nov 2023 - 3:37

61

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if $X$ is independent and $E(M) - X$ is coindependent, show that $X$ is a basis and $E(M) - X$ is a cobasis.

Published on 02 Dec 2023 - 19:53

73

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Showing the isomorphism between (the geometric lattice)$\pi_n$ and the lattice $\mathcal{L}(M(K_n)).$

Published on 03 Dec 2023 - 19:03

73

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Show that $C^*(e,B)$ is the unique cocircuit that is disjoint from $B - e.$

Published on 17 Dec 2023 - 17:16

72

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what will happen to the uniform matroid $U_{2,m}$ if we remove an element from it?

Published on 24 Dec 2023 - 20:29

83

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Partition lattice properties and an invariant.

Published on 25 Dec 2023 - 4:24

49

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what will happen if we contract an element in a uniform matroid?

Published on 26 Dec 2023 - 3:38

71

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Understanding how to find the dual of a matroid.

Published on 28 Dec 2023 - 6:04

54

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affine geometries that are self-dual matroids.

Published on 29 Dec 2023 - 8:34

40

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The basis of a regular matroid.

Published on 31 Dec 2023 - 4:45

List Question

Philip Hall's theorem

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

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

Taylor Expansion of the Polynomial in Flajolet’s Fundamental Lemma

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?

if $X$ is independent and $E(M) - X$ is coindependent, show that $X$ is a basis and $E(M) - X$ is a cobasis.

Showing the isomorphism between (the geometric lattice)$\pi_n$ and the lattice $\mathcal{L}(M(K_n)).$

Show that $C^*(e,B)$ is the unique cocircuit that is disjoint from $B - e.$

what will happen to the uniform matroid $U_{2,m}$ if we remove an element from it?

Partition lattice properties and an invariant.

what will happen if we contract an element in a uniform matroid?

Understanding how to find the dual of a matroid.

affine geometries that are self-dual matroids.

The basis of a regular matroid.

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