The signed Varchenko Determinant for Complexes of Oriented Matroids

TL;DR

This paper extends the concept of the Varchenko matrix to complexes of oriented matroids, demonstrating a factorization of its determinant that generalizes previous results on hyperplane arrangements.

Contribution

It introduces a generalized Varchenko matrix for complexes of oriented matroids and proves a new determinant factorization formula.

Findings

Determinant of the generalized Varchenko matrix factors nicely.

Extends known results from hyperplane arrangements to complexes of oriented matroids.

Provides a new algebraic tool for studying complexes of oriented matroids.

Abstract

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.