Low elements and small inversion sets are in bijection in rank 3 Coxeter groups

Publication date: 7 April 2021

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.

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Combinatorial aspects of groups and algebras (05E16)

This page was built for publication: Low elements and small inversion sets are in bijection in rank 3 Coxeter groups

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6364726)