对偶）对称反半群的克朗克系数

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of the Australian Mathematical Society Pub Date : 2024-09-13 DOI:10.1017/s1446788724000119

VOLODYMYR MAZORCHUK, SHRADDHA SRIVASTAVA

{"title":"对偶）对称反半群的克朗克系数","authors":"VOLODYMYR MAZORCHUK, SHRADDHA SRIVASTAVA","doi":"10.1017/s1446788724000119","DOIUrl":null,"url":null,"abstract":"<p>We study analogues of Kronecker coefficients for symmetric inverse semigroups, for dual symmetric inverse semigroups and for the inverse semigroups of bijections between subquotients of finite sets. In all cases, we reduce the problem of determination of such coefficients to some group-theoretic and combinatorial problems. For symmetric inverse semigroups, we provide an explicit formula in terms of the classical Kronecker and Littlewood–Richardson coefficients for symmetric groups.</p>","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"11 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"KRONECKER COEFFICIENTS FOR (DUAL) SYMMETRIC INVERSE SEMIGROUPS\",\"authors\":\"VOLODYMYR MAZORCHUK, SHRADDHA SRIVASTAVA\",\"doi\":\"10.1017/s1446788724000119\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study analogues of Kronecker coefficients for symmetric inverse semigroups, for dual symmetric inverse semigroups and for the inverse semigroups of bijections between subquotients of finite sets. In all cases, we reduce the problem of determination of such coefficients to some group-theoretic and combinatorial problems. For symmetric inverse semigroups, we provide an explicit formula in terms of the classical Kronecker and Littlewood–Richardson coefficients for symmetric groups.</p>\",\"PeriodicalId\":50007,\"journal\":{\"name\":\"Journal of the Australian Mathematical Society\",\"volume\":\"11 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-09-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Australian Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/s1446788724000119\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Australian Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s1446788724000119","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们研究了对称反半群、对偶对称反半群以及有限集的子项之间的双射的反半群的克罗内克系数的类似物。在所有情况下，我们都将确定这些系数的问题简化为一些群论和组合问题。对于对称反半群，我们用对称群的经典克罗内克系数和利特尔伍德-理查德森系数提供了一个明确的公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

KRONECKER COEFFICIENTS FOR (DUAL) SYMMETRIC INVERSE SEMIGROUPS

We study analogues of Kronecker coefficients for symmetric inverse semigroups, for dual symmetric inverse semigroups and for the inverse semigroups of bijections between subquotients of finite sets. In all cases, we reduce the problem of determination of such coefficients to some group-theoretic and combinatorial problems. For symmetric inverse semigroups, we provide an explicit formula in terms of the classical Kronecker and Littlewood–Richardson coefficients for symmetric groups.

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

Journal of the Australian Mathematical Society 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The Journal of the Australian Mathematical Society is the oldest journal of the Society, and is well established in its coverage of all areas of pure mathematics and mathematical statistics. It seeks to publish original high-quality articles of moderate length that will attract wide interest. Papers are carefully reviewed, and those with good introductions explaining the meaning and value of the results are preferred. Published Bi-monthly Published for the Australian Mathematical Society