The f-vector of a realizable matroid complex is strictly log-concave

Details The f-vector of a realizable matroid complex is strictly log-concave The f-vector of a realizable matroid complex is strictly log-concave

2011-06-15

arxiv.org/abs/1106.2944v3

Mathematics

Combinatorics

11 pages, minor corrections

Scientific paper

We show that f-vectors of matroid complexes of realizable matroids are strictly log-concave. This was conjectured by Mason in 1972. Our proof uses the recent result by Huh and Katz who showed that the coefficients of the characteristic polynomial of a realizable matroid form a log-concave sequence. We also prove a statement on log-concavity of h-vectors which strengthens a result by Brown and Colbourn. In the last two sections, we give a brief introduction to zonotopal algebra and we explain how it relates to our log-concavity results and various matroid/graph polynomials.

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