Richard Ehrenborg, Gábor Hetyei, Margaret A. Readdy
{"title":"加泰罗尼亚语--斯皮策排列","authors":"Richard Ehrenborg, Gábor Hetyei, Margaret A. Readdy","doi":"10.54550/eca2024v4s2r15","DOIUrl":null,"url":null,"abstract":"We study two classes of permutations intimately related to the visual proof of Spitzer's lemma and Huq's generalization of the Chung-Feller theorem. Both classes of permutations are counted by the Fuss-Catalan numbers. The study of one class leads to a generalization of results of Flajolet from continued fractions to continuants. The study of the other class leads to the discovery of a restricted variant of the Foata--Strehl group action.","PeriodicalId":340033,"journal":{"name":"Enumerative Combinatorics and Applications","volume":"3 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Catalan--Spitzer permutations\",\"authors\":\"Richard Ehrenborg, Gábor Hetyei, Margaret A. Readdy\",\"doi\":\"10.54550/eca2024v4s2r15\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study two classes of permutations intimately related to the visual proof of Spitzer's lemma and Huq's generalization of the Chung-Feller theorem. Both classes of permutations are counted by the Fuss-Catalan numbers. The study of one class leads to a generalization of results of Flajolet from continued fractions to continuants. The study of the other class leads to the discovery of a restricted variant of the Foata--Strehl group action.\",\"PeriodicalId\":340033,\"journal\":{\"name\":\"Enumerative Combinatorics and Applications\",\"volume\":\"3 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-09-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Enumerative Combinatorics and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.54550/eca2024v4s2r15\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Enumerative Combinatorics and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.54550/eca2024v4s2r15","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We study two classes of permutations intimately related to the visual proof of Spitzer's lemma and Huq's generalization of the Chung-Feller theorem. Both classes of permutations are counted by the Fuss-Catalan numbers. The study of one class leads to a generalization of results of Flajolet from continued fractions to continuants. The study of the other class leads to the discovery of a restricted variant of the Foata--Strehl group action.
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