h-Vectors of matroids and logarithmic concavity

h-Vectors of matroids and logarithmic concavity

Article history: Received 11 November 2012 Accepted 4 November 2014 Available online 13 November 2014 Communicated by Ezra Miller MSC: 05B35 52C35

Matroids and log-concavity

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 ...

Matroids: h-vectors, Zonotopes, and Lawrence Polytopes

Logarithmic Concavity and SI2(C)

We observe that for any logarithmically concave nite sequence a 0 , a 1 , : : : , a n of positive integers there is a representation of the Lie algebra sl 2 (C) from which this logarithmic concav-ity follows. Thus, in applying this strategy to prove logarithmic concavity, the only issue is to construct such a representation naturally from given combinatorial data. As an example, we do this when...

Generalized permutohedra , h - vectors of cotransversal matroids and pure O - sequences ( extended abstract )

Stanley has conjectured that the h-vector of a matroid complex is a pure O-sequence. We will prove this for cotransversal matroids by using generalized permutohedra. We construct a bijection between lattice points inside a r-dimensional convex polytope and bases of a rank r transversal matroid. Résumé. Stanley a conjecturé que le h-vecteur d’un complexe matroide est une pure O-séquence. Nous al...