4 papers
A family of rank non-algebraic matroids with pseudomodular dual
Winfried Hochstättler
The Tic-Tac-Toe matroid is a paving matroid of rank on 9 elements which is pseudomodular and whose dual is non-algebraic. It has been proposed as a possible example of an algeb…
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…
Lexicographic Extensions preserve Euclideaness
Winfried Hochstättler, Michael Wilhelmi
We prove that a lexicographical extension of a Euclidean oriented matroid remains Euclidean.
Vertex-shellings of Euclidean Oriented Matroids
Winfried Hochstättler, Michael Wilhelmi
A Euclidean oriented matroid program yields a partial ordering of the cocircuits of its cocircuit graph. We show that every linear extension of that ordering yields a topological s…