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
Weak Generalized Lifting Property, Bruhat Intervals, and Coxeter Matroids / Caselli, Fabrizio; D’Adderio, Michele; Marietti, Mario. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - STAMPA. - 2021:3(2021), pp. 1678-1698. [10.1093/imrn/rnaa124]
Weak Generalized Lifting Property, Bruhat Intervals, and Coxeter Matroids
Caselli, Fabrizio;
2021
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 polytopesFile in questo prodotto:
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