{"title":"正半有限矩阵中的广义对角线","authors":"Robert Angarone, Daniel Soskin","doi":"arxiv-2409.06907","DOIUrl":null,"url":null,"abstract":"We describe all inequalities among generalized diagonals in positive\nsemi-definite matrices. These turn out to be governed by a simple partial order\non the symmetric group. This provides an analogue of results of Drake, Gerrish,\nand Skandera on inequalities among generalized diagonals in totally nonnegative\nmatrices.","PeriodicalId":501407,"journal":{"name":"arXiv - MATH - Combinatorics","volume":"206 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generalized Diagonals in Positive Semi-Definite Matrices\",\"authors\":\"Robert Angarone, Daniel Soskin\",\"doi\":\"arxiv-2409.06907\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We describe all inequalities among generalized diagonals in positive\\nsemi-definite matrices. These turn out to be governed by a simple partial order\\non the symmetric group. This provides an analogue of results of Drake, Gerrish,\\nand Skandera on inequalities among generalized diagonals in totally nonnegative\\nmatrices.\",\"PeriodicalId\":501407,\"journal\":{\"name\":\"arXiv - MATH - Combinatorics\",\"volume\":\"206 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.06907\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06907","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Generalized Diagonals in Positive Semi-Definite Matrices
We describe all inequalities among generalized diagonals in positive
semi-definite matrices. These turn out to be governed by a simple partial order
on the symmetric group. This provides an analogue of results of Drake, Gerrish,
and Skandera on inequalities among generalized diagonals in totally nonnegative
matrices.
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