Characteristic polynomials of the weak order on classical and affine Coxeter groups
Combinatorics
2022-04-05 v1
Abstract
We find a simple product formula for the characteristic polynomial of the permutations with a fixed descent set under the weak order. As a corollary we obtain a simple product formula for the characteristic polynomial of alternating permutations. We generalize these results to Coxeter groups. We also find a formula for the generating function for the characteristic polynomials of classical Coxeter groups, which is then related to affine Coxeter groups.
Keywords
Cite
@article{arxiv.2204.01310,
title = {Characteristic polynomials of the weak order on classical and affine Coxeter groups},
author = {Jang Soo Kim and Sun-mi Yun},
journal= {arXiv preprint arXiv:2204.01310},
year = {2022}
}