{"title":"关于串并联矩阵的枚举","authors":"Nicholas Proudfoot , Yuan Xu , Benjamin Young","doi":"10.1016/j.aam.2024.102801","DOIUrl":null,"url":null,"abstract":"<div><div>By the work of Ferroni and Larson, Kazhdan–Lusztig polynomials and <em>Z</em>-polynomials of complete graphs have combinatorial interpretations in terms of quasi series-parallel matroids. We provide explicit formulas for the number of series-parallel matroids and the number of simple series-parallel matroids of a given rank and cardinality, extending results of Ferroni–Larson and Gao–Proudfoot–Yang–Zhang.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the enumeration of series-parallel matroids\",\"authors\":\"Nicholas Proudfoot , Yuan Xu , Benjamin Young\",\"doi\":\"10.1016/j.aam.2024.102801\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>By the work of Ferroni and Larson, Kazhdan–Lusztig polynomials and <em>Z</em>-polynomials of complete graphs have combinatorial interpretations in terms of quasi series-parallel matroids. We provide explicit formulas for the number of series-parallel matroids and the number of simple series-parallel matroids of a given rank and cardinality, extending results of Ferroni–Larson and Gao–Proudfoot–Yang–Zhang.</div></div>\",\"PeriodicalId\":50877,\"journal\":{\"name\":\"Advances in Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-10-30\",\"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/S0196885824001337\",\"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/S0196885824001337","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
根据费罗尼和拉尔森的研究成果，完整图的卡兹丹-卢兹提格多项式和 Z 多项式可以用准数列平行矩阵来组合解释。我们提供了给定秩和心数的数列平行矩阵数和简单数列平行矩阵数的明确公式，扩展了费罗尼-拉森和高-普鲁福-杨-张的结果。
By the work of Ferroni and Larson, Kazhdan–Lusztig polynomials and Z-polynomials of complete graphs have combinatorial interpretations in terms of quasi series-parallel matroids. We provide explicit formulas for the number of series-parallel matroids and the number of simple series-parallel matroids of a given rank and cardinality, extending results of Ferroni–Larson and Gao–Proudfoot–Yang–Zhang.
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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