{"title":"论卡兹丹-卢兹蒂格多项式中 q 的最小幂","authors":"Christian Gaetz , Yibo Gao","doi":"10.1016/j.aim.2024.109941","DOIUrl":null,"url":null,"abstract":"<div><p>For <em>w</em> in the symmetric group, we provide an exact formula for the smallest positive power <span><math><msup><mrow><mi>q</mi></mrow><mrow><mi>h</mi><mo>(</mo><mi>w</mi><mo>)</mo></mrow></msup></math></span> appearing in the Kazhdan–Lusztig polynomial <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>e</mi><mo>,</mo><mi>w</mi></mrow></msub><mo>(</mo><mi>q</mi><mo>)</mo></math></span>. We also provide a tight upper bound on <span><math><mi>h</mi><mo>(</mo><mi>w</mi><mo>)</mo></math></span> in simply-laced types, resolving a conjecture of Billey–Postnikov from 2002.</p></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the minimal power of q in a Kazhdan–Lusztig polynomial\",\"authors\":\"Christian Gaetz , Yibo Gao\",\"doi\":\"10.1016/j.aim.2024.109941\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>For <em>w</em> in the symmetric group, we provide an exact formula for the smallest positive power <span><math><msup><mrow><mi>q</mi></mrow><mrow><mi>h</mi><mo>(</mo><mi>w</mi><mo>)</mo></mrow></msup></math></span> appearing in the Kazhdan–Lusztig polynomial <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>e</mi><mo>,</mo><mi>w</mi></mrow></msub><mo>(</mo><mi>q</mi><mo>)</mo></math></span>. We also provide a tight upper bound on <span><math><mi>h</mi><mo>(</mo><mi>w</mi><mo>)</mo></math></span> in simply-laced types, resolving a conjecture of Billey–Postnikov from 2002.</p></div>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-09-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0001870824004560\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0001870824004560","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
On the minimal power of q in a Kazhdan–Lusztig polynomial
For w in the symmetric group, we provide an exact formula for the smallest positive power appearing in the Kazhdan–Lusztig polynomial . We also provide a tight upper bound on in simply-laced types, resolving a conjecture of Billey–Postnikov from 2002.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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