{"title":"Theorems of Carathéodory, Minkowski-Weyl, and Gordan up to Symmetry","authors":"D. Le, Tim Römer","doi":"10.1137/22M148865X","DOIUrl":null,"url":null,"abstract":"In this paper we extend three classical and fundamental results in polyhedral geometry, namely, Carath\\'{e}odory's theorem, the Minkowski-Weyl theorem, and Gordan's lemma to infinite dimensional spaces, in which considered cones and monoids are invariant under actions of symmetric groups.","PeriodicalId":48489,"journal":{"name":"SIAM Journal on Applied Algebra and Geometry","volume":"22 1","pages":"291-310"},"PeriodicalIF":1.6000,"publicationDate":"2021-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Applied Algebra and Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/22M148865X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 6
Abstract
In this paper we extend three classical and fundamental results in polyhedral geometry, namely, Carath\'{e}odory's theorem, the Minkowski-Weyl theorem, and Gordan's lemma to infinite dimensional spaces, in which considered cones and monoids are invariant under actions of symmetric groups.
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