List questions from algebraic-combinatorics

Published on 27 Sep 2023 - 23:53

89

Views

proving that $r(X \cup cl(Y)) = r(cl(X) \cup cl(Y)).$

Published on 28 Sep 2023 - 0:02

63

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Proving that $r(cl(X) \cup cl(Y)) = r(cl(X \cup Y))$.

Published on 28 Sep 2023 - 0:40

102

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If $X \subseteq Y$ and $r(X) = r(Y),$ then $cl(X) = cl(Y).$

Published on 02 Oct 2023 - 0:11

153

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circuit and a cocircuit can not have an odd number of common elements.

Published on 07 Oct 2023 - 2:41

51

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Show that a matroid $M$ is connected iff, for every pair of distinct elements of $E(M),$ there is a hyperplane avoiding both.

Published on 09 Oct 2023 - 10:24

103

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

Published on 11 Oct 2023 - 7:44

60

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Why every component of a loopless matroid is flat?

Published on 14 Oct 2023 - 17:41

40

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The relation between contraction and deletion in a matroid.

Published on 14 Oct 2023 - 20:21

84

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Determining all self-dual uniform matroids.

Published on 15 Oct 2023 - 2:29

82

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

Published on 19 Oct 2023 - 23:06

115

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

Published on 20 Oct 2023 - 12:09

80

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

Published on 20 Oct 2023 - 23:40

55

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Trace of power of matrix (arising from number of closed walks)

Published on 24 Oct 2023 - 14:07

58

Views

an $\mathbb F$- representation of the matroid $M_1 \oplus M_2.$

Published on 06 Nov 2023 - 11:45

List Question

proving that $r(X \cup Y) = r(X \cup cl(Y)).$

proving that $r(X \cup cl(Y)) = r(cl(X) \cup cl(Y)).$

Proving that $r(cl(X) \cup cl(Y)) = r(cl(X \cup Y))$.

If $X \subseteq Y$ and $r(X) = r(Y),$ then $cl(X) = cl(Y).$

circuit and a cocircuit can not have an odd number of common elements.

Show that a matroid $M$ is connected iff, for every pair of distinct elements of $E(M),$ there is a hyperplane avoiding both.

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.

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 $M^*.$

Trace of power of matrix (arising from number of closed walks)

an $\mathbb F$- representation of the matroid $M_1 \oplus M_2.$

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