{"title":"分块普法因子的非相交路径解释及其在倾斜正交多项式中的应用","authors":"Zong-Jun Yao, Shi-Hao Li","doi":"10.1016/j.aam.2024.102803","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we mainly consider a combinatoric explanation for block Pfaffians in terms of non-intersecting paths, as a generalization of results obtained by Stembridge. As applications, we demonstrate how are generating functions of non-intersecting paths related to skew orthogonal polynomials and their deformations, including a new concept called multiple partial-skew orthogonal polynomials.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"163 ","pages":"Article 102803"},"PeriodicalIF":1.0000,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Non-intersecting path explanation for block Pfaffians and applications into skew-orthogonal polynomials\",\"authors\":\"Zong-Jun Yao, Shi-Hao Li\",\"doi\":\"10.1016/j.aam.2024.102803\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we mainly consider a combinatoric explanation for block Pfaffians in terms of non-intersecting paths, as a generalization of results obtained by Stembridge. As applications, we demonstrate how are generating functions of non-intersecting paths related to skew orthogonal polynomials and their deformations, including a new concept called multiple partial-skew orthogonal polynomials.</div></div>\",\"PeriodicalId\":50877,\"journal\":{\"name\":\"Advances in Applied Mathematics\",\"volume\":\"163 \",\"pages\":\"Article 102803\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-11-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0196885824001350\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0196885824001350","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Non-intersecting path explanation for block Pfaffians and applications into skew-orthogonal polynomials
In this paper, we mainly consider a combinatoric explanation for block Pfaffians in terms of non-intersecting paths, as a generalization of results obtained by Stembridge. As applications, we demonstrate how are generating functions of non-intersecting paths related to skew orthogonal polynomials and their deformations, including a new concept called multiple partial-skew orthogonal polynomials.
期刊介绍：
Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas.
Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.
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