Unimodality questions for integrally closed lattice polytopes

Unimodality questions for integrally closed lattice polytopes

It is a famous open question whether every integrally closed reflexive polytope has a unimodal Ehrhart delta-vector. We generalize this question to arbitrary integrally closed lattice polytopes and we prove unimodality for the delta-vector of lattice parallelepipeds. This is the first nontrivial cla...

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Veröffentlicht in:arXiv.org 2011-10
Hauptverfasser: Schepers, Jan, Leen Van Langenhoven
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Parallelepipeds
Polytopes
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description It is a famous open question whether every integrally closed reflexive polytope has a unimodal Ehrhart delta-vector. We generalize this question to arbitrary integrally closed lattice polytopes and we prove unimodality for the delta-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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subjects Parallelepipeds
Polytopes
title Unimodality questions for integrally closed lattice polytopes
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