Noncommutative Schur functions for posets
Combinatorics
2022-11-10 v2 Rings and Algebras
Abstract
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 -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.
Keywords
Cite
@article{arxiv.2211.03967,
title = {Noncommutative Schur functions for posets},
author = {Jonah Blasiak and Holden Eriksson and Pavlo Pylyavskyy and Isaiah Siegl},
journal= {arXiv preprint arXiv:2211.03967},
year = {2022}
}