20 citations · 90 across the 12 of their papers we have counts for
12 papers · 1 filter
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…
A convolution formula for Tutte polynomials of arithmetic matroids and other combinatorial structures
Spencer Backman, Matthias Lenz
In this note we generalize the convolution formula for the Tutte polynomial of Kook-Reiner-Stanton and Etienne-Las Vergnas to a more general setting that includes both arithmetic m…
Splines, lattice points, and arithmetic matroids
Matthias Lenz
Let be a -matrix. We consider the variable polytope . It is known that the function that assigns to a parameter $u \in \math…
Lattice points in polytopes, box splines, and Todd operators
Matthias Lenz
Let be a list of vectors that is totally unimodular. In a previous article the author proved that every real-valued function on the set of interior lattice points of the zonoto…
Interpolation, box splines, and lattice points in zonotopes
Matthias Lenz
Let be a totally unimodular list of vectors in some lattice. Let be the box spline defined by . Its support is the zonotope . We show that any real-valued functi…
Zonotopal algebra and forward exchange matroids
Matthias Lenz
Zonotopal algebra is the study of a family of pairs of dual vector spaces of multivariate polynomials that can be associated with a list of vectors X. It connects objects from comb…
Matroids and log-concavity
Matthias Lenz
We show that f-vectors of matroid complexes of realisable matroids are log-concave. This was conjectured by Mason in 1972. Our proof uses the recent result by Huh and Katz who show…
Hierarchical zonotopal power ideals
Matthias Lenz
Zonotopal algebra deals with ideals and vector spaces of polynomials that are related to several combinatorial and geometric structures defined by a finite sequence of vectors. Giv…
Toric Ideals of Flow Polytopes
Matthias Lenz
A referee found an error in the proof of the Main Theorem ("toric ideals of flow polytopes are generated in degree 3") that we could not fix. More precisely, the proof of Lemma 4.2…