%0 Journal Article
%T Garside families in Artin-Tits monoids and low elements in Coxeter groups
%A Patrick Dehornoy
%A Matthew Dyer
%A Christophe Hohlweg
%J Mathematics
%D 2014
%I arXiv
%X We show that every finitely generated Artin-Tits group admits a finite Garside family, by introducing the notion of a low element in a Coxeter group and proving that the family of all low elements in a Coxeter system (W, S) with S finite includes S and is finite and closed under suffix and join with respect to the right weak order.
%U http://arxiv.org/abs/1411.7498v1