{"title":"从霍尔对易子理论看多重组合和的积分表示和计算","authors":"G. Egorychev, S. Kolesnikov, V. Leontiev","doi":"10.17516/1997-1397-2021-14-1-12-20","DOIUrl":null,"url":null,"abstract":"In this paper we prove a series of combinatorial identities arising from computing the exponents of the commutators in P. Hall’s collection formula. We also compute a sum in closed form that arises from using the collection formula in Chevalley groups for solving B. A. F. Wehrfritz problem on the regularity of their Sylow subgroups","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"26 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Integral Representation and the Computation of Multiple Combinatorial Sums from Hall’s Commutator Theory\",\"authors\":\"G. Egorychev, S. Kolesnikov, V. Leontiev\",\"doi\":\"10.17516/1997-1397-2021-14-1-12-20\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we prove a series of combinatorial identities arising from computing the exponents of the commutators in P. Hall’s collection formula. We also compute a sum in closed form that arises from using the collection formula in Chevalley groups for solving B. A. F. Wehrfritz problem on the regularity of their Sylow subgroups\",\"PeriodicalId\":43965,\"journal\":{\"name\":\"Journal of Siberian Federal University-Mathematics & Physics\",\"volume\":\"26 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2021-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Siberian Federal University-Mathematics & Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17516/1997-1397-2021-14-1-12-20\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Siberian Federal University-Mathematics & Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17516/1997-1397-2021-14-1-12-20","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
本文通过计算P. Hall集合公式中换向子的指数，证明了一系列组合恒等式。利用Chevalley群的集合公式求解B. a . F. Wehrfritz群的Sylow子群的正则性问题，得到一个封闭形式的和
Integral Representation and the Computation of Multiple Combinatorial Sums from Hall’s Commutator Theory
In this paper we prove a series of combinatorial identities arising from computing the exponents of the commutators in P. Hall’s collection formula. We also compute a sum in closed form that arises from using the collection formula in Chevalley groups for solving B. A. F. Wehrfritz problem on the regularity of their Sylow subgroups
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