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

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.

37 pages. To appear DMJ

Cited by in corpus (1)

• The permutahedral variety, mixed Eulerian numbers, and principal specializations of Schubert polynomials