Ehrhart series of polytopes related to symmetric doubly-stochastic matrices

Abstract

In Ehrhart theory, the h*-vector of a rational polytope often provides insights into properties of the polytope that may be otherwise obscured. As an example, the Birkho polytope, also known as the polytope of real doubly-stochastic matrices, has a unimodal h*-vector, but when even small modications are made to the polytope, the same property can be very dicult to prove. In this paper, we examine the h*-vectors of a class of polytopes containing real doubly-stochastic symmetric matrices.