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arXiv:1906.04719 [math.CO]AbstractReferencesReviewsResources

The $h^*$-polynomials of locally anti-blocking lattice polytopes and their $γ$-positivity

Hidefumi Ohsugi, Akiyoshi Tsuchiya

Published 2019-06-11Version 1

A lattice polytope $\mathcal{P} \subset \mathbb{R}^d$ is called a locally anti-blocking polytope if for any closed orthant $\mathbb{R}^d_{\varepsilon}$ in $\mathbb{R}^d$, $\mathcal{P} \cap \mathbb{R}^d_{\varepsilon}$ is unimodularly equivalent to an anti-blocking polytope by reflections of coordinate hyperplanes. In the present paper, we give a formula of the $h^*$-polynomials of locally anti-blocking lattice polytopes. In particular, we discuss the $\gamma$-positivity of the $h^*$-polynomials of locally anti-blocking reflexive polytopes.

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