2 citations · 2 across the 10 of their papers we have counts for
10 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.
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…
On the normally torsion-freeness of square-free monomial ideals
Mehrdad Nasernejad, Veronica Crispin Quiñonez, Winfried Hochstättler
Let be a square-free monomial ideal, be a prime monomial ideal in , be a square-free monomial in with $\mathrm{supp}(h) \…
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…
Positroids are 3-colorable
Lamar Chidiac, Winfried Hochstättler
We show that every positroid of rank has a good coline. Using the definition of the chromatic number of oriented matroid introduced by J.\ Nešetřil, R.\ Nickel, and W.~H…
Independent Hyperplanes in Oriented Paving Matroids
Lamar Chidiac, Winfried Hochstättler
In 1993, Csima and Sawyer proved that in a non-pencil arrangement of n pseudolines, there are at least simple points of intersection. Since pseudoline arrangements…
On the Geometry of Holmsen's Combinatorial Version of the Colorful Carathéodory
Helena Bergold, Winfried Hochstättler
Carathéodorys Theorem of convex hulls plays an important role in convex geometry. In 1982, Bárány formulated and proved a more general version, called the Colorful Carathéodory. Th…
Lattice Path Matroids are 3-Colorable
Immanuel Albrecht, Winfried Hochstättler
We show that every lattice path matroid of rank at least two has a quite simple coline, also known as a positive coline. Therefore every orientation of a lattice path matroid is 3-…