Ehrhart Series of Polytopes Related to Symmetric Doubly-Stochastic Matrices

Abstract

In Ehrhart theory, the $h^{\ast }$-vector of a rational polytope often provide insights into properties of the polytope that may be otherwise obscured. As an example, the Birkhoff polytope, also known as the polytope of real doubly-stochastic matrices, has a unimodal $h^{\ast }$-vector, but when even small modifications are made to the polytope, the same property can be very difficult to prove. In this paper, we examine the $h^{\ast }$-vectors of a class of polytopes containing real doubly-stochastic symmetric matrices.

11 pages; this revision removes an erroneous proposition from earlier versions and expands on the implications