Shellability of Kohnert posets
Combinatorics
2024-04-29 v1
Abstract
In this paper, we are concerned with identifying among the family of posets associated with Kohnert polynomials, those whose order complex has a certain combinatorial property. In particular, for numerous families of Kohnert polynomials, including key polynomials, we determine when the associated Kohnert posets are (EL-)shellable. Interestingly, under certain diagram restrictions, (EL-)shellability of a Kohnert poset is equivalent to multiplcity freeness of the associated Kohnert polynomial.
Cite
@article{arxiv.2404.17432,
title = {Shellability of Kohnert posets},
author = {Celia Kerr and Nicholas W. Mayers and Nicholas Russoniello},
journal= {arXiv preprint arXiv:2404.17432},
year = {2024}
}