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In Ehrhart theory, the $h^*$-vector of a rational polytope often provideinsights into properties of the polytope that may be otherwise obscured. As anexample, the Birkhoff polytope, also known as the polytope of realdoubly-stochastic matrices, has a unimodal $h^*$-vector, but when even smallmodifications are made to the polytope, the same property can be very difficultto prove. In this paper, we examine the $h^*$-vectors of a class of polytopescontaining real doubly-stochastic symmetric matrices.

Ehrhart Series of Polytopes Related to Symmetric Doubly-Stochastic Matrices