通过气泡实现格罗内迪克多项式的 M-凸性

IF 0.9 3区数学 Q2 MATHEMATICS SIAM Journal on Discrete Mathematics Pub Date : 2024-07-23 DOI:10.1137/23m1599082

Elena S. Hafner, Karola Mészáros, Linus Setiabrata, Avery St. Dizier

{"title":"通过气泡实现格罗内迪克多项式的 M-凸性","authors":"Elena S. Hafner, Karola Mészáros, Linus Setiabrata, Avery St. Dizier","doi":"10.1137/23m1599082","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2194-2225, September 2024. <br/> Abstract. We introduce bubbling diagrams and show that they compute the support of the Grothendieck polynomial of any vexillary permutation. Using these diagrams, we show that the support of the top homogeneous component of such a Grothendieck polynomial coincides with the support of the dual character of an explicit flagged Weyl module. We also show that the homogenized Grothendieck polynomial of a vexillary permutation has M-convex support.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"M-Convexity of Vexillary Grothendieck Polynomials via Bubbling\",\"authors\":\"Elena S. Hafner, Karola Mészáros, Linus Setiabrata, Avery St. Dizier\",\"doi\":\"10.1137/23m1599082\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2194-2225, September 2024. <br/> Abstract. We introduce bubbling diagrams and show that they compute the support of the Grothendieck polynomial of any vexillary permutation. Using these diagrams, we show that the support of the top homogeneous component of such a Grothendieck polynomial coincides with the support of the dual character of an explicit flagged Weyl module. We also show that the homogenized Grothendieck polynomial of a vexillary permutation has M-convex support.\",\"PeriodicalId\":49530,\"journal\":{\"name\":\"SIAM Journal on Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-07-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/23m1599082\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1599082","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

摘要

SIAM 离散数学杂志》，第 38 卷第 3 期，第 2194-2225 页，2024 年 9 月。摘要我们引入了冒泡图，并证明冒泡图可以计算任意矢量置换的格罗顿第克多项式的支持。利用这些图，我们证明了这样一个格罗内狄克多项式的顶同质分量的支持与一个明确标记的韦尔模块的对偶特征的支持重合。我们还证明了矢量置换的同源格罗内狄克多项式具有 M-凸支持。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

M-Convexity of Vexillary Grothendieck Polynomials via Bubbling

SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2194-2225, September 2024.
Abstract. We introduce bubbling diagrams and show that they compute the support of the Grothendieck polynomial of any vexillary permutation. Using these diagrams, we show that the support of the top homogeneous component of such a Grothendieck polynomial coincides with the support of the dual character of an explicit flagged Weyl module. We also show that the homogenized Grothendieck polynomial of a vexillary permutation has M-convex support.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.

期刊最新文献

An Algorithm to Recover Shredded Random Matrices On Powers of Hamilton Cycles in Ramsey–Turán Theory Maximum Number of Symmetric Extensions in Random Graphs Graphs of Degree at Least [math] with Minimum Algebraic Connectivity On the Turán Number of Edge Blow-Ups of Cliques