{"title":"花环产品同一性的多面体证明","authors":"Robert Davis, B. Sagan","doi":"10.4310/JOC.2019.V10.N4.A5","DOIUrl":null,"url":null,"abstract":"In 2013, Beck and Braun proved and generalized multiple identities involving permutation statistics via discrete geometry. Namely, they recognized the identities as specializations of integer point transform identities for certain polyhedral cones. They extended many of their proof techniques to obtain identities involving wreath products, but some identities were resistant to their proof attempts. In this article, we provide a geometric justification of one of these wreath product identities, which was first established by Biagioli and Zeng.","PeriodicalId":44683,"journal":{"name":"Journal of Combinatorics","volume":"8 3","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2017-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A polyhedral proof of a wreath product identity\",\"authors\":\"Robert Davis, B. Sagan\",\"doi\":\"10.4310/JOC.2019.V10.N4.A5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In 2013, Beck and Braun proved and generalized multiple identities involving permutation statistics via discrete geometry. Namely, they recognized the identities as specializations of integer point transform identities for certain polyhedral cones. They extended many of their proof techniques to obtain identities involving wreath products, but some identities were resistant to their proof attempts. In this article, we provide a geometric justification of one of these wreath product identities, which was first established by Biagioli and Zeng.\",\"PeriodicalId\":44683,\"journal\":{\"name\":\"Journal of Combinatorics\",\"volume\":\"8 3\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2017-12-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4310/JOC.2019.V10.N4.A5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/JOC.2019.V10.N4.A5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
In 2013, Beck and Braun proved and generalized multiple identities involving permutation statistics via discrete geometry. Namely, they recognized the identities as specializations of integer point transform identities for certain polyhedral cones. They extended many of their proof techniques to obtain identities involving wreath products, but some identities were resistant to their proof attempts. In this article, we provide a geometric justification of one of these wreath product identities, which was first established by Biagioli and Zeng.
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