Generalized Permutohedra, h-Vectors of Cotransversal Matroids and Pure O-Sequences

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 an r-dimensional convex polytope and bases of a rank r transversal matroid.