Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4653255 | European Journal of Combinatorics | 2016 | 19 Pages |
Abstract
In this article, we investigate the existence of joins in the weak order of an infinite Coxeter group WW. We give a geometric characterization of the existence of a join for a subset XX in WW in terms of the inversion sets of its elements and their position relative to the imaginary cone. Finally, we discuss inversion sets of infinite reduced words and the notions of biconvex and biclosed sets of positive roots.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Christophe Hohlweg, Jean-Philippe Labbé,