Unimodality Questions for Integrally Closed Lattice Polytopes

By Jan Schepers, Leen van Langenhoven. 2011

65 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5a943aa9c43beb613fc7b87a05b0207dd13b7146

How researchers see this paper

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In Algebra and Number Theory

1. Liam Solus
2. Petter Brand'en
3. Benjamin Braun

In Discrete Mathematics and Combinatorics

1. Liam Solus
2. Petter Brand'en
3. Benjamin Braun
4. Julius Borcea

In Geometry and Topology

1. Benjamin Braun
2. Liam Solus
3. Petter Brand'en
4. Julius Borcea

Citations in the corpus

• Symmetric Decompositions and Real-Rootedness (2018, background): “In [30], the authors verified Conjecture 4.”
• Unimodality problems in Ehrhart theory (2015, background): “Another approach to provingh∗-unimodality for IDP reflexive polytopes was proposed by Schepers and Van Langenhoven [62].”