Proper elements of Coxeter groups
Combinatorics
2025-09-18 v3
Abstract
We extend the notion of proper elements to all Coxeter groups. For all infinite families of finite Coxeter groups we prove that the probability a random element is proper goes to zero in the limit. This proves a conjecture of the third author and A. Yong regarding the proportion of Schubert varieties that are Levi spherical for all infinite families of Weyl groups. We also enumerate the proper elements in the exceptional Coxeter groups.
Keywords
Cite
@article{arxiv.2111.15105,
title = {Proper elements of Coxeter groups},
author = {József Balogh and David Brewster and Reuven Hodges},
journal= {arXiv preprint arXiv:2111.15105},
year = {2025}
}
Comments
21 pages