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arXiv · 1209.3575

Matroid base polytope decomposition II : sequence of hyperplane splits

Vanessa Chatelain·Jorge Ramirez Alfonsin
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Abstract

This is a continuation of the early paper concerning matroid base polytope decomposition. Here, we will present sufficient conditions on $M$ so its base matroid polytope $P(M)$ has a {\em sequence} of hyperplane splits. The latter yields to decompositions of $P(M)$ with two or more pieces for infinitely many matroids $M$. We also present necessary conditions on the Euclidean representation of rank three matroids $M$ for the existences of decompositions of $P(M)$ into $2$ or $3$ pieces. Finally, we prove that $P(M_1 \oplus M_2)$ has a sequence of hyperplane splits if either $P(M_1)$ or $P(M_2)$ also has a sequence of hyperplane splits.

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Vanessa Chatelain, Jorge Ramirez Alfonsin. 2012-09-17. Matroid base polytope decomposition II : sequence of hyperplane splits. https://arxiv.org/abs/1209.3575

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