Weak Generalized Lifting Property, Bruhat Intervals, and Coxeter Matroids. (12th June 2020) - Caselli, Fabrizio; D'Adderio, Michele; Marietti, Mario
Abstract: We provide a weaker version of the generalized lifting property that holds in complete generality for all 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.