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arXiv 1906.04719math.CO
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局部反阻塞格多面体的$h^*$ -多项式及其$γ$ -正性

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

Hidefumi Ohsugi, Akiyoshi Tsuchiya

备注：
19 pages, Explanations and references are added. Writings are improved
发表信息：
Discrete and Computational Geometry 66 (2021), 701--722
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摘要：

格多面体$\mathcal{P} \subset \mathbb{R}^d$称为局部防阻塞多面体，如果对$\mathbb{R}^d$中的任意闭正交$\mathbb{R}^d_{\varepsilon}$，$\mathcal{P} \cap \mathbb{R}^d_{\varepsilon}$通过坐标超平面的反射单模等价于防阻塞多面体.本文给出了局部反阻塞格多面体的$h^*$ -多项式的一个公式。特别地，我们讨论了局部防阻塞自反多面体的$h^*$ -多项式的$γ$ -正性。

英文摘要：

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 for the $h^*$-polynomials of locally anti-blocking lattice polytopes. In particular, we discuss the $γ$-positivity of the $h^*$-polynomials of locally anti-blocking reflexive polytopes.

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