{"title":"一些可积分晶格模型的瑞尔丹阵列族","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":"{\"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}","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}
A Riordan array family for some integrable lattice models
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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