Convex caterpillars are Schur-Positive
Combinatorics
2020-06-15 v3
Abstract
A remarkable result of Stanley shows that the set of maximal chains in the non-crossing partition lattice of type is Schur-positive, where descents are defined by a distinguished edge labeling. A bijection between these chains and labeled trees was presented by Goulden and Yong. Using Adin-Roichman's variant of Bj\"orner's -labeling, we show that the subset of maximal chains in the non-crossing partition lattice of type , whose underlying tree is a convex caterpillar, is Schur-positive.
Keywords
Cite
@article{arxiv.1812.09863,
title = {Convex caterpillars are Schur-Positive},
author = {Yuval Hovannes Khachatryan-Raziel},
journal= {arXiv preprint arXiv:1812.09863},
year = {2020}
}