The Varchenko determinant for oriented matroids

DOI10.1007/s00209-019-02275-zzbMath1428.52026arXiv1805.07183OpenAlexW2964111989MaRDI QIDQ2332882

Volkmar Welker, Winfried Hochstättler

Publication date: 5 November 2019

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.07183

zbMATH Keywords

oriented matroidhyperplane arrangementVarchenko matrixsupertope

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Combinatorial aspects of matroids and geometric lattices (05B35) Semimodular lattices, geometric lattices (06C10) Oriented matroids in discrete geometry (52C40) Configurations and arrangements of linear subspaces (14N20) Gale and other diagrams (52B35)

Related Items (6)

The Varchenko determinant of an oriented matroid ⋮ The Varchenko matrix for topoplane arrangements ⋮ The Varchenko determinant for apartments ⋮ On the Varchenko determinant formula for oriented braid arrangements ⋮ Corners and simpliciality in oriented matroids and partial cubes ⋮ Two-dimensional partial cubes

Cites Work

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• The Varchenko determinant of a Coxeter arrangement
• Arrangements of hyperplanes and Lie algebra homology
• Realizability of a model in infinite statistics
• The determinant formula for a matroid bilinear form
• COMs: complexes of oriented matroids
• Bilinear form of real configuration of hyperplanes
• A $q$-deformation of a trivial symmetric group action
• Topics in Hyperplane Arrangements
• Oriented Matroids

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