Matroid base polytope decomposition II : sequence of hyperplane splits

2012/09/17 by Chatelain, Vanessa, Alfonsin, Jorge Ramirez
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1209.3575

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(M₁ ⊕ M₂) has a sequence of hyperplane splits if either P(M₁) or P(M₂) also has a sequence of hyperplane splits.

Related

• Matroid base polytope decomposition
• Flag enumerations of matroid base polytopes
• The Weak-Map Order and Polytopal Decompositions of Matroid Base Polytopes
• Hypergraph characterization of split matroids
• Generalized Splitting and element splitting operations on p-matroids