20 citations · 90 across the 12 of their papers we have counts for
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Stanley-Reisner rings for quasi-arithmetic matroids
Matthias Lenz
In this note we define a Stanley-Reisner ring for quasi-arithmetic matroids and more general structures. To this end, we define two types of CW complexes associated with a quasi-ar…
Computing the poset of layers of a toric arrangement
Matthias Lenz
A toric arrangement is an arrangement of subtori of codimension one in a real or complex torus. The poset of layers is the set of connected components of non-empty intersections of…
Representations of weakly multiplicative arithmetic matroids are unique
Matthias Lenz
An arithmetic matroid is weakly multiplicative if the multiplicity of at least one of its bases is equal to the product of the multiplicities of its elements. We show that if such…
On powers of Plücker coordinates and representability of arithmetic matroids
Matthias Lenz
The first problem we investigate is the following: given and a vector of Plücker coordinates of a point in the real Grassmannian, is the vector obtain…