8 citations · 50 across the 16 of their papers we have counts for
16 papers
Free line arrangements with low maximal multiplicity
Alexandru Dimca, Lukas Kühne, Piotr Pokora
Let $\A$ be a free arrangement of lines in the complex projective plane, with exponents . Let be the maximal multiplicity of points in $\A$. In this note, we d…
Dynamical systems on some elliptic modular surfaces via operators on line arrangements
Lukas Kühne, Xavier Roulleau
This paper further studies the matroid realization space of a specific deformation of the regular -gon with its lines of symmetry. Recently, we obtained that these particular re…
Line arrangements with many triple points
Lukas Kühne, Tomasz Szemberg, Halszka Tutaj-Gasińska
In this paper, we construct an infinite series of line arrangements in characteristic two, each featuring only triple intersection points. This finding challenges the existing conj…
Projective dimension of weakly chordal graphic arrangements
Takuro Abe, Lukas Kühne, Paul Mücksch +1
A graphic arrangement is a subarrangement of the braid arrangement whose set of hyperplanes is determined by an undirected graph. A classical result due to Stanley, Edelman and Rei…
Faces of Cosmological Polytopes
Lukas Kühne, Leonid Monin
A cosmological polytope is a lattice polytope introduced by Arkani-Hamed, Benincasa, and Postnikov in their study of the wavefunction of the universe in a class of cosmological mod…
On entropic and almost multilinear representability of matroids
Lukas Kühne, Geva Yashfe
This article studies two notions of generalized matroid representations motivated by algorithmic information theory and cryptographic secret sharing. The first (entropic representa…
Computing the nonfree locus of the moduli space of arrangements and Terao's freeness conjecture
Mohamed Barakat, Lukas Kühne
In this paper, we show how to compute using Fitting ideals the nonfree locus of the moduli space of arrangements of a rank simple matroid, i.e., the subset of all points of the…
On the geometry of flag Hilbert-Poincaré series for matroids
Lukas Kühne, Joshua Maglione
We extend the definition of coarse flag Hilbert--Poincaré series to matroids; these series arise in the context of local Igusa zeta functions associated to hyperplane arrangements.…
Likelihood Degenerations
Daniele Agostini, Taylor Brysiewicz, Claudia Fevola +3
Computing all critical points of a monomial on a very affine variety is a fundamental task in algebraic statistics, particle physics and other fields. The number of critical points…
Computing characteristic polynomials of hyperplane arrangements with symmetries
Taylor Brysiewicz, Holger Eble, Lukas Kühne
We introduce a new algorithm computing the characteristic polynomials of hyperplane arrangements which exploits their underlying symmetry groups. Our algorithm counts the chambers…
Von Staudt Constructions for Skew-Linear and Multilinear Matroids
Lukas Kühne, Rudi Pendavingh, Geva Yashfe
This paper compares skew-linear and multilinear matroid representations. These are matroids that are representable over division rings and (roughly speaking) invertible matrices, r…
The Universality of the Resonance Arrangement and its Betti Numbers
Lukas Kühne
The resonance arrangement is the arrangement of hyperplanes which has all non-zero -vectors in as normal vectors. It is the adjoint of the Braid…
Representability of Matroids by c-Arrangements is Undecidable
Lukas Kühne, Geva Yashfe
For a natural number , a -arrangement is an arrangement of dimension subspaces satisfying the following condition: the sum of any subset of the subspaces has dimension a…
On the generation of rank 3 simple matroids with an application to Terao's freeness conjecture
Mohamed Barakat, Reimer Behrends, Christopher Jefferson +2
In this paper we describe a parallel algorithm for generating all non-isomorphic rank simple matroids with a given multiplicity vector. We apply our implementation in the HPC v…
Locally Heavy Hyperplanes in Multiarrangements
Takuro Abe, Lukas Kühne
Hyperplane Arrangements of rank admitting an unbalanced Ziegler restriction are known to fulfill Terao's conjecture. This long-standing conjecture asks whether the freeness of…
Heavy hyperplanes in multiarrangements and their freeness
Takuro Abe, Lukas Kühne
Only few categories of free arrangements are known in which Terao's conjecture holds. One of such categories consists of -arrangements with unbalanced Ziegler restrictions. In t…