A Tverberg type theorem for matroids

2016/07/06 by Imre Bárány, Gil Kalai, Bárány, Imre +3
Mathematics · #05E45 (Secondary) #52A35 (Primary) #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05E45 #msc:52A35

paper · pdf · doi:10.48550/arxiv.1607.01599

This article is due to be published in the collection of papers "A Journey through Discrete Mathematics. A Tribute to Jiri Matousek" edited by Martin Loebl, Jaroslav Nesetril and Robin Thomas, due to be published by Springer

arxiv created 2016/11/27 · arxiv updated 2016/11/29

Abstract

Let b(M) denote the maximal number of disjoint bases in a matroid M. It is shown that if M is a matroid of rank d+1, then for any continuous map f from the matroidal complex M into the d-dimensional Euclidean space there exist t ≥ √(b(M))/4 disjoint independent sets σ₁,…,σ_t ∈ M such that \bigcap_i=1^t f(σ_i) ≠ ∅.

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