1 citations · 1 across the 4 of their papers we have counts for
4 papers
Exploring the Varchenko Determinant of Partial Cubes
Winfried Hochstättler, Sophia Keip, Birol Yazici
The Varchenko matrix is known to have a well-structured determinant for complexes of oriented matroids (COMs). COMs can be characterized as partial cubes that do not have certain f…
The Chain Matrix of Bouquets of Geometric Lattices and its Determinant
Winfried Hochstättler, Sophia Keip
This work builds on Varchenko et al's introduction of bilinear forms for hyperplane arrangements, where the determinant of the associated matrices factorizes into simple components…
The signed Varchenko Determinant for Complexes of Oriented Matroids
Winfried Hochstättler, Sophia Keip, Kolja Knauer
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 previ…
Kirchberger's Theorem for Complexes of Oriented Matroids
Winfried Hochstättler, Sophia Keip, Kolja Knauer
The separation theorem of Kirchberger can be proven using a combination of Farkas' Lemma and Caratheodory's Theorem. Since those theorems are at the heart of oriented matroids, we…