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The signed Varchenko Determinant for Complexes of Oriented Matroids

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arxiv 2211.13986 v3 pith:4N2U6VHL submitted 2022-11-25 math.CO math.AG

Winfried Hochstättler , Sophia Keip , Kolja Knauer This is my paper · ORCID
classification math.COmath.AG
keywords matroidsorientedcomplexesdeterminanthyperplanesignedvarchenkoarrangement
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We generalize the (signed) Varchenko matrix of a hyperplane arrangement to complexes of oriented matroids and show that its determinant has a nice factorization. This extends previous results on hyperplane arrangements and oriented matroids.

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  1. The Chain Matrix of Bouquets of Geometric Lattices and its Determinant

    math.CO 2024-11 conditional novelty 6.0 of 10

    The determinant of the chain matrix of a bouquet of geometric lattices equals, up to sign, a product of linear weight functions raised to cumulated rho exponents.

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