{"title":"Ehrhart Quasi-Polynomials of Almost Integral Polytopes","authors":"Christopher de Vries, Masahiko Yoshinaga","doi":"10.1007/s00454-023-00604-y","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"126 8","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete & Computational Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00454-023-00604-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 3
Abstract
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.
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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