Lattice polytopes, Hecke operators, and the Ehrhart polynomial

2004/05/29 by Paul E. Gunnells, Gunnells, Paul E., Fernando Rodriguez Villegas +1 · 1 citation
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.math/0405573

24 pp

arxiv created 2004/05/29 · arxiv updated 2009/12/01

Abstract

Let P be a simple lattice polytope. We define an action of the Hecke operators on E (P), the Ehrhart polynomial of P, and describe their effect on the coefficients of E (P). We also describe how the Brion-Vergne formula transforms under the Hecke operators for nonsingular lattice polytopes P.

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