Zobrazeno 1 - 10
of 57
pro vyhledávání: '"Kühne, Lukas"'
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 polytopes'' or ``Kantorovich-Rubinstein polytopes'' in the literature. A
Externí odkaz:
http://arxiv.org/abs/2408.15584
Autor:
Degen, Sebastian, Kühne, Lukas
A $q$-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 $q$-matroids are motivated by coding theory as the representable $q$-matroids ar
Externí odkaz:
http://arxiv.org/abs/2408.06795
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 consists of a pair of two arrangements with $13$ lines. Moreover, we use th
Externí odkaz:
http://arxiv.org/abs/2407.07070
Autor:
Kühne, Lukas, Roulleau, Xavier
This paper further studies the matroid realization space of a specific deformation of the regular $n$-gon with its lines of symmetry. Recently, we obtained that these particular realization spaces are birational to the elliptic modular surfaces $\Xi_
Externí odkaz:
http://arxiv.org/abs/2402.18207
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 conjecture that suggests the existence of only a finite number of such arr
Externí odkaz:
http://arxiv.org/abs/2401.14766
Autor:
Kühne, Lukas, Roulleau, Xavier
We investigate the matroid realization space of a specific deformation of the regular $n$-gon with its lines of symmetry. It turns out that these particular realization spaces are birational to the elliptic modular surfaces $\Xi_{1}(n)$ over the modu
Externí odkaz:
http://arxiv.org/abs/2312.03470
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 geometry), Polymake (polyhedral geometry), and Antic (number theory). Here,
Externí odkaz:
http://arxiv.org/abs/2311.08792
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 Reiner states that a graphic arrangement is free if and only if the corre
Externí odkaz:
http://arxiv.org/abs/2307.06021
Autor:
Kühne, Lukas, Monin, Leonid
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 models. More concretely, they construct a cosmological polytope for any F
Externí odkaz:
http://arxiv.org/abs/2209.08069
Autor:
Cuntz, Michael, Kühne, Lukas
We investigate arrangements of hyperplanes whose normal vectors are given by connected subgraphs of a fixed graph. These include the resonance arrangement and certain ideal subarrangements of Weyl arrangements. We characterize those which are free, s
Externí odkaz:
http://arxiv.org/abs/2208.09251