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Matthias Beck (MSRI)

Coefficients and Roots of Ehrhart Polynomials

Abstract for the Combinatorics and Number Theory Seminar 2003 November 10 (Note special day.)

The Ehrhart polynomial of a lattice polytope counts integer points in integral dilates of the polytope. The coefficients of these polynomials are, for the most part, a complete mystery. We have established linear inequalities between the coefficients of an Ehrhart polynomial, depending only on the dimension of the polytope. These relations imply, in particular, that in a fixed dimension the roots of any Ehrhart polynomial are bounded. Our result can be generalized slightly, to Poincaré series of a certain type.

Furthermore, we give partially tight bounds for the real roots of an Ehrhart polynomial.

Finally, I will report on studies of special classes of polytopes whose Ehrhart polynomials exhibit remarkable behavior.

This is joint work with Mike Develin (Berkeley), Jesus DeLoera (Davis), and Julian Pfeifle (Barcelona).

seminars/comb/abstract.200311beck.txt · Last modified: 2020/01/29 14:03 (external edit)