Unimodality Questions for Integrally Closed Lattice Polytopes |
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Authors: | Jan Schepers Leen Van Langenhoven |
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Institution: | 1. KU Leuven, Celestijnenlaan 200B, 3001, Leuven, Belgium
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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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