Scholarlink

<p>The machinery of noncommutative Schur functions is a general approach to Schur positivity of symmetric functions initiated by Fomin-Greene. Hwang recently adapted this theory to posets to give a new approach to the Stanley-Stembridge conjecture. We further develop this theory to prove that the symmetric function associated to any <i>P</i>-Knuth equivalence graph is Schur positive. This settles a conjecture of Kim and the third author, and refines results of Gasharov, Shareshian-Wachs, and Hwang on the Schur positivity of chromatic symmetric functions.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Noncommutative Schur functions for posets

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年1月24日

查看全文
  • J. Blasiak,
  • H. Eriksson,
  • P. Pylyavskyy,
  • I. Siegl

摘要

The machinery of noncommutative Schur functions is a general approach to Schur positivity of symmetric functions initiated by Fomin-Greene. Hwang recently adapted this theory to posets to give a new approach to the Stanley-Stembridge conjecture. We further develop this theory to prove that the symmetric function associated to any P-Knuth equivalence graph is Schur positive. This settles a conjecture of Kim and the third author, and refines results of Gasharov, Shareshian-Wachs, and Hwang on the Schur positivity of chromatic symmetric functions.