M. Archibald, A. Blecher, Sergi Elizalde, A. Knopfmacher
{"title":"亚对角和超对角分区","authors":"M. Archibald, A. Blecher, Sergi Elizalde, A. Knopfmacher","doi":"10.1007/s13370-025-01282-0","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we consider weakly monotonic sequences of positive integers <span>\\(\\lambda _1,\\lambda _2,\\dots ,\\lambda _k\\)</span> such that either <span>\\(\\lambda _i\\le i\\)</span> for all <i>i</i> (subdiagonal partitions) or <span>\\(\\lambda _i\\ge i\\)</span> for all <i>i</i> (superdiagonal partitions). We provide generating functions for these partitions with respect to size and number of parts, using various approaches involving multivariate generating functions, functional equations, area statistics on lattice paths, and bijections.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 2","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13370-025-01282-0.pdf","citationCount":"0","resultStr":"{\"title\":\"Subdiagonal and superdiagonal partitions\",\"authors\":\"M. Archibald, A. Blecher, Sergi Elizalde, A. Knopfmacher\",\"doi\":\"10.1007/s13370-025-01282-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper we consider weakly monotonic sequences of positive integers <span>\\\\(\\\\lambda _1,\\\\lambda _2,\\\\dots ,\\\\lambda _k\\\\)</span> such that either <span>\\\\(\\\\lambda _i\\\\le i\\\\)</span> for all <i>i</i> (subdiagonal partitions) or <span>\\\\(\\\\lambda _i\\\\ge i\\\\)</span> for all <i>i</i> (superdiagonal partitions). We provide generating functions for these partitions with respect to size and number of parts, using various approaches involving multivariate generating functions, functional equations, area statistics on lattice paths, and bijections.</p></div>\",\"PeriodicalId\":46107,\"journal\":{\"name\":\"Afrika Matematika\",\"volume\":\"36 2\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2025-04-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s13370-025-01282-0.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Afrika Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13370-025-01282-0\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Afrika Matematika","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s13370-025-01282-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
In this paper we consider weakly monotonic sequences of positive integers \(\lambda _1,\lambda _2,\dots ,\lambda _k\) such that either \(\lambda _i\le i\) for all i (subdiagonal partitions) or \(\lambda _i\ge i\) for all i (superdiagonal partitions). We provide generating functions for these partitions with respect to size and number of parts, using various approaches involving multivariate generating functions, functional equations, area statistics on lattice paths, and bijections.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
