{"title":"奇数强度球形设计达到法泽卡斯-列文斯丹边界的覆盖和普遍最小电位","authors":"Sergiy Borodachov","doi":"10.1007/s00010-024-01036-6","DOIUrl":null,"url":null,"abstract":"<div><p>We characterize the cases of existence of spherical designs of an odd strength attaining the Fazekas–Levenshtein bound for covering and prove some of their properties. We also find all universal minima of the potential of regular spherical configurations in two new cases: the demihypercube on <span>\\(S^d\\)</span>, <span>\\(d\\ge 4\\)</span>, and the <span>\\(2_{41}\\)</span> polytope on <span>\\(S^7\\)</span> (which is dual to the <span>\\(E_8\\)</span> lattice).\n</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01036-6.pdf","citationCount":"0","resultStr":"{\"title\":\"Odd strength spherical designs attaining the Fazekas–Levenshtein bound for covering and universal minima of potentials\",\"authors\":\"Sergiy Borodachov\",\"doi\":\"10.1007/s00010-024-01036-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We characterize the cases of existence of spherical designs of an odd strength attaining the Fazekas–Levenshtein bound for covering and prove some of their properties. We also find all universal minima of the potential of regular spherical configurations in two new cases: the demihypercube on <span>\\\\(S^d\\\\)</span>, <span>\\\\(d\\\\ge 4\\\\)</span>, and the <span>\\\\(2_{41}\\\\)</span> polytope on <span>\\\\(S^7\\\\)</span> (which is dual to the <span>\\\\(E_8\\\\)</span> lattice).\\n</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-03-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00010-024-01036-6.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00010-024-01036-6\",\"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://link.springer.com/article/10.1007/s00010-024-01036-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Odd strength spherical designs attaining the Fazekas–Levenshtein bound for covering and universal minima of potentials
We characterize the cases of existence of spherical designs of an odd strength attaining the Fazekas–Levenshtein bound for covering and prove some of their properties. We also find all universal minima of the potential of regular spherical configurations in two new cases: the demihypercube on \(S^d\), \(d\ge 4\), and the \(2_{41}\) polytope on \(S^7\) (which is dual to the \(E_8\) lattice).
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