{"title":"Involutions containing exactly r pairs of intersecting arcs","authors":"T. Mansour","doi":"10.47443/dml.2022.046","DOIUrl":null,"url":null,"abstract":"Abstract The generating function Fr(x) that counts the involutions on n letters containing exactly r pairs of intersecting arcs in their graphical representation is studied. More precisely, an algorithm that computes the generating function Fr(x) for any given r ≥ 0 is presented. To derive the result for a given r, the algorithm performs certain routine checks on involutions of length 2r + 2 without fixed points. The algorithm is implemented in Maple and yields explicit formulas for 0 ≤ r ≤ 4.","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2022-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics Letters","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47443/dml.2022.046","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract The generating function Fr(x) that counts the involutions on n letters containing exactly r pairs of intersecting arcs in their graphical representation is studied. More precisely, an algorithm that computes the generating function Fr(x) for any given r ≥ 0 is presented. To derive the result for a given r, the algorithm performs certain routine checks on involutions of length 2r + 2 without fixed points. The algorithm is implemented in Maple and yields explicit formulas for 0 ≤ r ≤ 4.
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