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Lattice polytopes, Hecke operators, and the Ehrhart polynomial

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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 for E(P) transforms under the Hecke operators for nonsingular lattice polytopes P.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, 01003, USA

    Paul E. Gunnells

  2. Department of Mathematics, University of Texas, Austin, TX, 78712, USA

    Fernando Rodriguez Villegas

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  1. Paul E. Gunnells
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  2. Fernando Rodriguez Villegas
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Correspondence to Paul E. Gunnells.

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Gunnells, P.E., Villegas, F.R. Lattice polytopes, Hecke operators, and the Ehrhart polynomial. Sel. math., New ser. 13, 253 (2007). https://doi.org/10.1007/s00029-007-0037-5

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  • DOI: https://doi.org/10.1007/s00029-007-0037-5

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