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arXiv · 1106.2944

Matroids and log-concavity

Matthias Lenz
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Abstract

We show that f-vectors of matroid complexes of realisable matroids are 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 realisable matroid form a log-concave sequence. We also discuss the relationship between log-concavity of f-vectors and h-vectors of matroids. In the last section we explain the connection between zonotopal algebra and f-vectors and characteristic polynomials of matroids.

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Matthias Lenz. 2013-06-10. Matroids and log-concavity. https://arxiv.org/abs/1106.2944

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