{"title":"Skew Dyck paths with air pockets","authors":"Jean-Luc Baril, Rémi Maréchal, Helmut Prodinger","doi":"10.1007/s00010-024-01065-1","DOIUrl":null,"url":null,"abstract":"<div><p>We yield bivariate generating function for the number of <i>n</i>-length partial skew Dyck paths with air pockets (DAPs) ending at a given ordinate. We also give an asymptotic approximation for the average ordinate of the endpoint in all partial skew DAPs of a given length. Similar studies are made for two subclasses of skew DAPs, namely valley-avoiding and zigzagging, valley-avoiding skew DAPs. We express these results as Riordan arrays. Finally, we present two one-to-one correspondences with binary words avoiding the patterns 00 and 0110, and palindromic compositions with parts in <span>\\(\\{2,1,3,5,7,\\ldots \\}\\)</span>.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 1","pages":"257 - 274"},"PeriodicalIF":0.7000,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Aequationes Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00010-024-01065-1","RegionNum":3,"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
We yield bivariate generating function for the number of n-length partial skew Dyck paths with air pockets (DAPs) ending at a given ordinate. We also give an asymptotic approximation for the average ordinate of the endpoint in all partial skew DAPs of a given length. Similar studies are made for two subclasses of skew DAPs, namely valley-avoiding and zigzagging, valley-avoiding skew DAPs. We express these results as Riordan arrays. Finally, we present two one-to-one correspondences with binary words avoiding the patterns 00 and 0110, and palindromic compositions with parts in \(\{2,1,3,5,7,\ldots \}\).
期刊介绍：
aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.
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