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arXiv · 2008.01121

The Universal Valuation of Coxeter Matroids

Christopher Eur·Mario Sanchez·Mariel Supina
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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.

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Christopher Eur, Mario Sanchez, Mariel Supina. 2020-08-03. The Universal Valuation of Coxeter Matroids. https://doi.org/10.1112/blms.12461

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