1 citations · 2 across the 6 of their papers we have counts for
8 papers
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…
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…
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…
Combinatorial invariants of finite metric spaces and the Wasserstein arrangement
Emanuele Delucchi, Lukas Kühne, Leonie Mühlherr
In 2010, Vershik proposed a new combinatorial invariant of metric spaces given by a class of polytopes that arise in the theory of optimal transport and are called ``Wasserstein po…
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…
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…
Matroids in OSCAR
Daniel Corey, Lukas Kühne, Benjamin Schröter
OSCAR is an innovative new computer algebra system which combines and extends the power of its four cornerstone systems - GAP (group theory), Singular (algebra and algebraic geomet…