Littlewood-Richardson系数和plethystic系数正的必要条件

IF 0.8 4区数学 Q2 MATHEMATICS Comptes Rendus Mathematique Pub Date : 2023-10-24 DOI:10.5802/crmath.468

Álvaro Gutiérrez, Mercedes H. Rosas

{"title":"Littlewood-Richardson系数和plethystic系数正的必要条件","authors":"Álvaro Gutiérrez, Mercedes H. Rosas","doi":"10.5802/crmath.468","DOIUrl":null,"url":null,"abstract":"We give necessary conditions for the positivity of Littlewood–Richardson coefficients and SXP coefficients. We deduce necessary conditions for the positivity of the plethystic coefficients. Explicitly, our main result states that if S λ (V) appears as a summand in the decomposition into irreducibles of S μ (S ν (V)), then ν’s diagram is contained in λ’s diagram.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":"12 3","pages":"0"},"PeriodicalIF":0.8000,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients\",\"authors\":\"Álvaro Gutiérrez, Mercedes H. Rosas\",\"doi\":\"10.5802/crmath.468\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give necessary conditions for the positivity of Littlewood–Richardson coefficients and SXP coefficients. We deduce necessary conditions for the positivity of the plethystic coefficients. Explicitly, our main result states that if S λ (V) appears as a summand in the decomposition into irreducibles of S μ (S ν (V)), then ν’s diagram is contained in λ’s diagram.\",\"PeriodicalId\":10620,\"journal\":{\"name\":\"Comptes Rendus Mathematique\",\"volume\":\"12 3\",\"pages\":\"0\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-10-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus Mathematique\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5802/crmath.468\",\"RegionNum\":4,\"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":"Comptes Rendus Mathematique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/crmath.468","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

给出了Littlewood-Richardson系数和SXP系数正的必要条件。我们推导出多倍体系数为正的必要条件。明确地，我们的主要结果表明，如果S λ (V)在S μ (S ν (V))的不可约分解中以求和形式出现，则ν的图包含在λ的图中。

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

Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients

We give necessary conditions for the positivity of Littlewood–Richardson coefficients and SXP coefficients. We deduce necessary conditions for the positivity of the plethystic coefficients. Explicitly, our main result states that if S λ (V) appears as a summand in the decomposition into irreducibles of S μ (S ν (V)), then ν’s diagram is contained in λ’s diagram.

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

Comptes Rendus Mathematique 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

115

审稿时长

16.6 weeks

期刊介绍： The Comptes Rendus - Mathématique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, … Articles are original notes that briefly describe an important discovery or result. The articles are written in French or English. The journal also publishes review papers, thematic issues and texts reflecting the activity of Académie des sciences in the field of Mathematics.