Unimodality questions for integrally closed lattice polytopes

Details Unimodality questions for integrally closed lattice polytopes Unimodality questions for integrally closed lattice polytopes

2011-10-17

arxiv.org/abs/1110.3724v1

Mathematics

Combinatorics

16 pages

Scientific paper

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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