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

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#combinatorics #graph-theory #matroids #algebraic-combinatorics #graphic-matroids
90
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proving that $r(X \cup cl(Y)) = r(cl(X) \cup cl(Y)).$

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#combinatorics #graph-theory #matroids #algebraic-combinatorics #graphic-matroids
64
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Proving that $r(cl(X) \cup cl(Y)) = r(cl(X \cup Y))$.

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#combinatorics #graph-theory #matroids #algebraic-combinatorics #graphic-matroids
103
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If $X \subseteq Y$ and $r(X) = r(Y),$ then $cl(X) = cl(Y).$

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#linear-algebra #combinatorics #graph-theory #matroids #algebraic-combinatorics
154
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circuit and a cocircuit can not have an odd number of common elements.

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#combinatorics #graph-theory #matroids #algebraic-combinatorics #graphic-matroids
52
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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.

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#combinatorics #graph-theory #algebraic-combinatorics #graphic-matroids
104
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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
61
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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
41
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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
85
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Determining all self-dual uniform matroids.

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#combinatorics #discrete-mathematics #graph-theory #matroids #algebraic-combinatorics
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
116
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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
81
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Finding an $\mathbb R$-representation for $M^*.$

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#linear-algebra #matrices #graph-theory #matroids #algebraic-combinatorics
56
Views

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

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#graph-theory #algebraic-combinatorics #adjacency-matrix
59
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an $\mathbb F$- representation of the matroid $M_1 \oplus M_2.$

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#linear-algebra #graph-theory #combinatorial-geometry #algebraic-combinatorics

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