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It is proved that for a certain class of integer polytopes P the polynomial h(t ) which appears as the numerator in the Ehrhart series of P, when written as a rational function of t, is equal to the h-polynomial of a simplicial polytope and hence that its co-efficients satisfy the conditions of the g-theorem. This class includes the order polytopes of graded posets, previously studied by Reiner and Welker, and the Birkhoff polytope of doubly stochastic n × n matrices. In the latter case the unimodality of the coefficients of h (t ), which follows, was conjectured by Stanley in 1983.
Published Online: 2005-11-07
Published in Print: 2005-06-27
© Walter de Gruyter