{"title":"将积分凸集分解为有界和圆锥积分凸集的闵科夫斯基和","authors":"Kazuo Murota, Akihisa Tamura","doi":"10.1007/s13160-023-00635-1","DOIUrl":null,"url":null,"abstract":"<p>Every polyhedron can be decomposed into a Minkowski sum (or vector sum) of a bounded polyhedron and a polyhedral cone. This paper establishes similar statements for some classes of discrete sets in discrete convex analysis, such as integrally convex sets, <span>\\(\\hbox {L}^{\\natural }\\)</span>-convex sets, and <span>\\(\\hbox {M}^{\\natural }\\)</span>-convex sets.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Decomposition of an integrally convex set into a Minkowski sum of bounded and conic integrally convex sets\",\"authors\":\"Kazuo Murota, Akihisa Tamura\",\"doi\":\"10.1007/s13160-023-00635-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Every polyhedron can be decomposed into a Minkowski sum (or vector sum) of a bounded polyhedron and a polyhedral cone. This paper establishes similar statements for some classes of discrete sets in discrete convex analysis, such as integrally convex sets, <span>\\\\(\\\\hbox {L}^{\\\\natural }\\\\)</span>-convex sets, and <span>\\\\(\\\\hbox {M}^{\\\\natural }\\\\)</span>-convex sets.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-12-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s13160-023-00635-1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13160-023-00635-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Decomposition of an integrally convex set into a Minkowski sum of bounded and conic integrally convex sets
Every polyhedron can be decomposed into a Minkowski sum (or vector sum) of a bounded polyhedron and a polyhedral cone. This paper establishes similar statements for some classes of discrete sets in discrete convex analysis, such as integrally convex sets, \(\hbox {L}^{\natural }\)-convex sets, and \(\hbox {M}^{\natural }\)-convex sets.
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