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Licensed Unlicensed Requires Authentication Published by De Gruyter November 7, 2005

Ehrhart polynomials, simplicial polytopes, magic squares and a conjecture of Stanley

  • Christos A. Athanasiadis
From the journal


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 (t ), which follows, was conjectured by Stanley in 1983.

Published Online: 2005-11-07
Published in Print: 2005-06-27

© Walter de Gruyter

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