{"title":"Covering the permutohedron by affine hyperplanes","authors":"G. Hegedüs, GY. Károlyi","doi":"10.1007/s10474-024-01462-7","DOIUrl":null,"url":null,"abstract":"<p>An almost cover of a finite set in the affine space is a collection\nof hyperplanes that together cover all points of the set except one. Using the\npolynomial method, we determine the minimum size of an almost cover of the\nvertex set of the permutohedron and address a few related questions.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"16 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10474-024-01462-7","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
An almost cover of a finite set in the affine space is a collection
of hyperplanes that together cover all points of the set except one. Using the
polynomial method, we determine the minimum size of an almost cover of the
vertex set of the permutohedron and address a few related questions.
期刊介绍：
Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.
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