Symmetric edge polytopes are not gamma-positive

Luis Ferroni

Symmetric edge polytopes are not gamma-positive

Combinatorics 2026-07-02 v1

Authors: Luis Ferroni

Abstract

A conjecture posed by Ohsugi and Tsuchiya (2019) postulates that the Ehrhart $h^*$ -polynomials of symmetric edge polytopes are $\gamma$ -positive. We disprove this conjecture by exhibiting an infinite family of counterexamples. The smallest example provided by our construction is a $36$ -dimensional symmetric edge polytope.

Keywords

symmetric edge polytopes Ehrhart polynomials gamma-positivity counterexamples

Cite

@article{arxiv.2607.02424,
  title  = {Symmetric edge polytopes are not gamma-positive},
  author = {Luis Ferroni},
  journal= {arXiv preprint arXiv:2607.02424},
  year   = {2026}
}

Comments

6 pages, 1 Figure. Comments welcome!