### 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.

**Comments:**18 pages

**Categories:**math.CO

arXiv:1810.12258 [math.CO] (Published 2018-10-29)

Reflexive polytopes arising from bipartite graphs with $γ$-positivity associated to interior polynomials

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arXiv:1812.01910 [math.CO] (Published 2018-12-05)

A formula for $F$-Polynomials in terms of $C$-Vectors and Stabilization of $F$-Polynomials