6 papers
Addition theorems for Ziegler pairs of hyperplane arrangements
Takuro Abe, Lukas Kühne, Piotr Pokora
Inspired by Terao's freeness conjecture, we examine Ziegler pairs, which are pairs of hyperplane arrangements that share the same underlying matroid but have different modules of l…
Absolute incidence theorems and tilings
Lukas Kühne, Matt Larson
We give a precise definition of incidence theorems in plane projective geometry and introduce the notion of ``absolute incidence theorems,'' which hold over any ring. Fomin and Pyl…
On the numerical Terao's conjecture and Ziegler pairs for line arrangements
Lukas Kühne, Dante Luber, Piotr Pokora
In this paper we present a smallest possible counterexample to the Numerical Terao's Conjecture in the class of line arrangements in the complex projective plane. Our example consi…
Regular polygons, line operators, and elliptic modular surfaces as realization spaces of matroids
Lukas Kühne, Xavier Roulleau
For an integer , we investigate the matroid realization space of a specific deformation of the regular -gon along with its lines of symmetry. It turns out that this par…
Most -matroids are not representable
Sebastian Degen, Lukas Kühne
A -matroid is the analogue of a matroid which arises by replacing the finite ground set of a matroid with a finite-dimensional vector space over a finite field. These -matroi…
When alcoved polytopes add
Nick Early, Lukas Kühne, Leonid Monin
Alcoved polytopes are characterized by the property that all facet normal directions are parallel to the roots . Unlike other prominent families of polytopes, like general…