几乎整多边形的Ehrhart拟多项式

IF 0.6 3区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS Discrete & Computational Geometry Pub Date : 2023-11-24 DOI:10.1007/s00454-023-00604-y

Christopher de Vries, Masahiko Yoshinaga

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引用次数: 3

摘要

由有理向量平移的晶格多面体称为几乎整多面体。本文研究了概整多边形的Ehrhart拟多项式。研究了多面体的形状与Ehrhart拟多项式的代数性质之间的联系。特别地，我们证明了点阵带拓扑和中心对称点阵多面体是由它们的有理平移的Ehrhart拟多项式表征的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Ehrhart Quasi-Polynomials of Almost Integral Polytopes

A lattice polytope translated by a rational vector is called an almost integral polytope. In this paper, we study Ehrhart quasi-polynomials of almost integral polytopes. We study the connection between the shape of polytopes and the algebraic properties of the Ehrhart quasi-polynomials. In particular, we prove that lattice zonotopes and centrally symmetric lattice polytopes are characterized by Ehrhart quasi-polynomials of their rational translations.

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来源期刊

Discrete & Computational Geometry 数学-计算机：理论方法

CiteScore

1.80

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Discrete & Computational Geometry (DCG) is an international journal of mathematics and computer science, covering a broad range of topics in which geometry plays a fundamental role. It publishes papers on such topics as configurations and arrangements, spatial subdivision, packing, covering, and tiling, geometric complexity, polytopes, point location, geometric probability, geometric range searching, combinatorial and computational topology, probabilistic techniques in computational geometry, geometric graphs, geometry of numbers, and motion planning.

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