{"title":"条形核心分区的推广","authors":"Dean Yates","doi":"10.5802/alco.231","DOIUrl":null,"url":null,"abstract":"When p and q are coprime odd integers no less than 3, Olsson proved that the q -bar-core of a p -bar-core is again a p -bar-core. We establish a generalisation of this theorem: that the p -bar-weight of the q -bar-core of a bar partition λ is at most the p -bar-weight of λ . We go on to study the set of bar partitions for which equality holds and show that it is a union of orbits for an action of a Coxeter group of type ˜ C ( p − 1) / 2 × ˜ C ( q − 1) / 2 . We also provide an algorithm for constructing a bar partition in this set with a given p -bar-core and q -bar-core.","PeriodicalId":36046,"journal":{"name":"Algebraic Combinatorics","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"A generalisation of bar-core partitions\",\"authors\":\"Dean Yates\",\"doi\":\"10.5802/alco.231\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"When p and q are coprime odd integers no less than 3, Olsson proved that the q -bar-core of a p -bar-core is again a p -bar-core. We establish a generalisation of this theorem: that the p -bar-weight of the q -bar-core of a bar partition λ is at most the p -bar-weight of λ . We go on to study the set of bar partitions for which equality holds and show that it is a union of orbits for an action of a Coxeter group of type ˜ C ( p − 1) / 2 × ˜ C ( q − 1) / 2 . We also provide an algorithm for constructing a bar partition in this set with a given p -bar-core and q -bar-core.\",\"PeriodicalId\":36046,\"journal\":{\"name\":\"Algebraic Combinatorics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-09-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebraic Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5802/alco.231\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebraic Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/alco.231","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
When p and q are coprime odd integers no less than 3, Olsson proved that the q -bar-core of a p -bar-core is again a p -bar-core. We establish a generalisation of this theorem: that the p -bar-weight of the q -bar-core of a bar partition λ is at most the p -bar-weight of λ . We go on to study the set of bar partitions for which equality holds and show that it is a union of orbits for an action of a Coxeter group of type ˜ C ( p − 1) / 2 × ˜ C ( q − 1) / 2 . We also provide an algorithm for constructing a bar partition in this set with a given p -bar-core and q -bar-core.
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