{"title":"On a Characterization of Lattice Cubes via Discrete Isoperimetric Inequalities","authors":"D. Iglesias, E. Lucas","doi":"10.37236/11024","DOIUrl":null,"url":null,"abstract":"We obtain a characterization of lattice cubes as the only sets that reach equality in several discrete isoperimetric-type inequalities associated with the $L_{\\infty}$ norm, including well-known results by Radcliffe and Veomett. We furthermore provide a new isoperimetric inequality for the lattice point enumerator that generalizes previous results, and for which the aforementioned characterization also holds.","PeriodicalId":11515,"journal":{"name":"Electronic Journal of Combinatorics","volume":"2013 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.37236/11024","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We obtain a characterization of lattice cubes as the only sets that reach equality in several discrete isoperimetric-type inequalities associated with the $L_{\infty}$ norm, including well-known results by Radcliffe and Veomett. We furthermore provide a new isoperimetric inequality for the lattice point enumerator that generalizes previous results, and for which the aforementioned characterization also holds.
IF 5.3 2区 生物学Human GeneticsPub Date : 2002-12-01DOI: 10.1007/s00439-002-0809-0
Mellissa M C DeMille, Judith R Kidd, Valeria Ruggeri, Meg A Palmatier, David Goldman, Adekunle Odunsi, Friday Okonofua, Elena Grigorenko, Leslie O Schulz, Batsheva Bonne-Tamir, Ru-Band Lu, Josef Parnas, Andrew J Pakstis, Kenneth K Kidd
期刊介绍：
The Electronic Journal of Combinatorics (E-JC) is a fully-refereed electronic journal with very high standards, publishing papers of substantial content and interest in all branches of discrete mathematics, including combinatorics, graph theory, and algorithms for combinatorial problems.
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