Low elements and small inversion sets are in bijection in rank 3 Coxeter groups
Combinatorics
2022-01-26 v1 Group Theory
Abstract
In this extended abstract we announce a proof that, in a Coxeter group of rank 3, low elements are in bijection with small inversion sets. This gives a partial confirmation of Conjecture 2 in [Dyer, Hohlweg '16]. That same article provides the main ingredient: the bipodality of the set of small roots is used to propagate information on the vertices of inversion polytopes.
Cite
@article{arxiv.2104.03040,
title = {Low elements and small inversion sets are in bijection in rank 3 Coxeter groups},
author = {Balthazar Charles},
journal= {arXiv preprint arXiv:2104.03040},
year = {2022}
}
Comments
12 pages, 7 figures