Ehrhart Polynomial Roots and Stanley's Non-negativity Theorem

Details Ehrhart Polynomial Roots and Stanley's Non-negativity Theorem Ehrhart Polynomial Roots and Stanley's Non-negativity Theorem

2006-10-12

arxiv.org/abs/math/0610399v1

Integer points in polyhedra--geometry, number theory, representation theory, algebra, optimization, statistics, 67--78, Contem

Mathematics

Combinatorics

11 pages, submitted

Scientific paper

Stanley's non-negativity theorem is at the heart of many of the results in Ehrhart theory. In this paper, we analyze the root behavior of general polynomials satisfying the conditions of Stanley's theorem and compare this to the known root behavior of Ehrhart polynomials. We provide a possible counterexample to a conjecture of the second author, M. Beck, J. De Loera, J. Pfeifle, and R. Stanley, and contribute some experimental data as well.

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