论卡兹丹-卢兹蒂格多项式中 q 的最小幂

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-10 DOI:10.1016/j.aim.2024.109941

Christian Gaetz , Yibo Gao

引用次数: 0

摘要

对于对称群中的 w，我们提供了卡兹丹-卢兹提格多项式 Pe,w(q)中出现的最小正幂次 qh(w) 的精确公式。我们还提供了简并类型中 h(w) 的严密上限，解决了比列-波斯特尼科夫（Billey-Postnikov）在 2002 年提出的一个猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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 $q^{h (w)}$ appearing in the Kazhdan–Lusztig polynomial $P_{e, w} (q)$ . We also provide a tight upper bound on $h (w)$ in simply-laced types, resolving a conjecture of Billey–Postnikov from 2002.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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.