{"title":"关于Jack多项式的Schur展开的一些猜想","authors":"P. Alexandersson, J. Haglund, George Wang","doi":"10.4310/joc.2021.v12.n2.a2","DOIUrl":null,"url":null,"abstract":"We present positivity conjectures for the Schur expansion of Jack symmetric functions in two bases given by binomial coefficients. Partial results suggest that there are rich combinatorics to be found in these bases, including Eulerian numbers, Stirling numbers, quasi-Yamanouchi tableaux, and rook boards. These results also lead to further conjectures about the fundamental quasisymmetric expansions of these bases, which we prove for special cases.","PeriodicalId":44683,"journal":{"name":"Journal of Combinatorics","volume":"49 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2018-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Some conjectures on the Schur expansion of Jack polynomials\",\"authors\":\"P. Alexandersson, J. Haglund, George Wang\",\"doi\":\"10.4310/joc.2021.v12.n2.a2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present positivity conjectures for the Schur expansion of Jack symmetric functions in two bases given by binomial coefficients. Partial results suggest that there are rich combinatorics to be found in these bases, including Eulerian numbers, Stirling numbers, quasi-Yamanouchi tableaux, and rook boards. These results also lead to further conjectures about the fundamental quasisymmetric expansions of these bases, which we prove for special cases.\",\"PeriodicalId\":44683,\"journal\":{\"name\":\"Journal of Combinatorics\",\"volume\":\"49 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2018-10-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4310/joc.2021.v12.n2.a2\",\"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.2021.v12.n2.a2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Some conjectures on the Schur expansion of Jack polynomials
We present positivity conjectures for the Schur expansion of Jack symmetric functions in two bases given by binomial coefficients. Partial results suggest that there are rich combinatorics to be found in these bases, including Eulerian numbers, Stirling numbers, quasi-Yamanouchi tableaux, and rook boards. These results also lead to further conjectures about the fundamental quasisymmetric expansions of these bases, which we prove for special cases.
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