3 papers
math.CO2025
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…
math.CO2024
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…
math.CO2024
On simple matroids with a unique minimal tropical basis
Winfried Hochstättler
In this note we characterize tropical bases as sets of circuits that by orthogonality determine the set of cocircuits of a simple matroid. Furthermore, we show that any circuit, wh…