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Unimodality Questions for Integrally Closed Lattice Polytopes

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Abstract

It is a famous open question whether every integrally closed reflexive polytope has a unimodal Ehrhart δ -vector. We generalize this question to arbitrary integrally closed lattice polytopes and we prove unimodality for the δ -vector of lattice parallelepipeds. This is the first nontrivial class of integrally closed polytopes. Moreover, we suggest a new approach to the problem for reflexive polytopes via triangulations.

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Authors and Affiliations

  1. KU Leuven, Celestijnenlaan 200B, 3001, Leuven, Belgium

    Jan Schepers & Leen Van Langenhoven

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  1. Jan Schepers
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  2. Leen Van Langenhoven
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Correspondence to Jan Schepers.

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The first named author is a Postdoctoral Fellow of the Research Foundation - Flanders (FWO).

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Schepers, J., Van Langenhoven, L. Unimodality Questions for Integrally Closed Lattice Polytopes. Ann. Comb. 17, 571–589 (2013). https://doi.org/10.1007/s00026-013-0185-6

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  • DOI: https://doi.org/10.1007/s00026-013-0185-6

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