{"title":"A Riordan array family for some integrable lattice models","authors":"Paul Barry","doi":"arxiv-2409.09547","DOIUrl":null,"url":null,"abstract":"We study a family of Riordan arrays whose square symmetrizations lead to the\nRobbins numbers as well as numbers associated to the $20$ vertex model. We\nprovide closed-form expressions for the elements of these arrays, and also give\na canonical Catalan factorization for them. We describe a related family of\nRiordan arrays whose symmetrizations also lead to the same integer sequences.","PeriodicalId":501407,"journal":{"name":"arXiv - MATH - Combinatorics","volume":"10 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09547","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We study a family of Riordan arrays whose square symmetrizations lead to the
Robbins numbers as well as numbers associated to the $20$ vertex model. We
provide closed-form expressions for the elements of these arrays, and also give
a canonical Catalan factorization for them. We describe a related family of
Riordan arrays whose symmetrizations also lead to the same integer sequences.
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