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The universal valuation of Coxeter matroids
Department of Mathematics Stanford University 450 Jane Stanford Way, Building 380 Stanford CA 94305 USA.
Department of Mathematics University of California Berkeley 970 Evans Hall Berkeley CA 94720 USA.
Department of Mathematics University of California Berkeley 970 Evans Hall Berkeley CA 94720 USA.ORCID iD: 0000-0002-4816-590X
2021 (English)In: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 53, no 3, p. 798-819Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Wiley , 2021. Vol. 53, no 3, p. 798-819
National Category
Algebra and Logic Discrete Mathematics Geometry
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-312706DOI: 10.1112/blms.12461ISI: 000608410100001Scopus ID: 2-s2.0-85099434818OAI: oai:DiVA.org:kth-312706DiVA, id: diva2:1659685
Note

QC 20220621

Available from: 2022-05-20 Created: 2022-05-20 Last updated: 2024-03-18Bibliographically approved

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Supina, Mariel

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