Weak generalized lifting property, Bruhat intervals and Coxeter matroids
arXiv:1904.10208
Abstract
We provide a weaker version of the generalized lifting property which holds in complete generality for all finite Coxeter groups, and we use it to show that every parabolic Bruhat interval of a finite Coxeter group is a Coxeter matroid. We also describe some combinatorial properties of the associated polytopes.
13 pages