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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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

Christos A. Athanasiadis1


Citation Information: Journal für die reine und angewandte Mathematik. Volume 2005, Issue 583, Pages 163–174, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crll.2005.2005.583.163, November 2005

Publication History

8. März 2004
Published Online:


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.

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