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arXiv · 2005.01937

Log-concavity of matroid h-vectors and mixed Eulerian numbers

Andrew Berget·Hunter Spink·Dennis Tseng
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Abstract

For any matroid $M$, we compute the Tutte polynomial $T_M(x,y)$ using the mixed intersection numbers of certain classes in the combinatorial Chow ring $A^\bullet(M)$ arising from hypersimplices. Using the mixed Hodge-Riemann relations, we deduce a strengthening of the log-concavity of the $h$-vector of a matroid complex, improving on an old conjecture of Dawson.

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Andrew Berget, Hunter Spink, Dennis Tseng. 2020-05-05. Log-concavity of matroid h-vectors and mixed Eulerian numbers. https://arxiv.org/abs/2005.01937

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