The universal valuation of Coxeter matroids. Issue 3 (18th January 2021)

• Record Type: Journal Article
• Authors: Eur, Christopher; Sanchez, Mario; Supina, Mariel
• Is Part Of: Bulletin of the London Mathematical Society. Volume 53:Issue 3(2021)
• Page Start: 798
• Page End: 819
• Publication Date: 2021-01-18
• Subjects: 20F55 -- 52B40 -- 52B45 (primary); Mathematics -- Periodicals; 510
• DOI: 10.1112/blms.12461
• Languages: English
• ISSNs: 0024-6093

Abstract

Abstract: Coxeter matroids generalize matroids just as flag varieties of Lie groups generalize Grassmannians. Valuations of Coxeter matroids are functions that behave well with respect to subdivisions of a Coxeter matroid into smaller ones. We compute the universal valuative invariant of Coxeter matroids. A key ingredient is the family of Coxeter Schubert matroids, which correspond to the Bruhat cells of flag varieties. In the process, we compute the universal valuation of generalized Coxeter permutohedra, a larger family of polyhedra that model Coxeter analogues of combinatorial objects such as matroids, clusters, and posets.