Séminaire Lotharingien de Combinatoire, 85B.51 (2021), 12 pp.
Balthazar Charles
Low Elements and Small Inversion Sets are in Bijection in Rank 3 Coxeter Groups
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.
Received: December 1, 2020.
Accepted: March 1, 2021.
Final version: April 29, 2021.
The following versions are available: