Alessandro Iraci, Roberto Pagaria, Giovanni Paolini, Anna Vanden Wyngaerd
{"title":"Rectangular analogues of the square paths conjecture and the univariate Delta conjecture","authors":"Alessandro Iraci, Roberto Pagaria, Giovanni Paolini, Anna Vanden Wyngaerd","doi":"10.5070/c63261980","DOIUrl":null,"url":null,"abstract":"In this paper, we extend the rectangular side of the shuffle conjecture by stating a rectangular analogue of the square paths conjecture. In addition, we describe a set of combinatorial objects and one statistic that are a first step towards a rectangular extension of (the rise version of) the Delta conjecture, and of (the rise version of) the Delta square conjecture, corresponding to the case \\(q=1\\) of an expected general statement. We also prove our new rectangular paths conjecture in the special case when the sides of the rectangle are coprime.Mathematics Subject Classifications: 05E05Keywords: Macdonald polynomials, symmetric functions","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory Series A","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5070/c63261980","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we extend the rectangular side of the shuffle conjecture by stating a rectangular analogue of the square paths conjecture. In addition, we describe a set of combinatorial objects and one statistic that are a first step towards a rectangular extension of (the rise version of) the Delta conjecture, and of (the rise version of) the Delta square conjecture, corresponding to the case \(q=1\) of an expected general statement. We also prove our new rectangular paths conjecture in the special case when the sides of the rectangle are coprime.Mathematics Subject Classifications: 05E05Keywords: Macdonald polynomials, symmetric functions
期刊介绍:
The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.