A bound for crystallographic arrangements
Combinatorics
2019-03-04 v1 Quantum Algebra
Abstract
A crystallographic arrangement is a set of linear hyperplanes satisfying a certain integrality property and decomposing the space into simplicial cones. Crystallographic arrangements were completely classified in a series of papers by Heckenberger and the author. However, this classification is based on two computer proofs checking millions of cases. In the present paper, we prove without using a computer that, up to equivalence, there are only finitely many irreducible crystallographic arrangements in each rank greater than two.
Cite
@article{arxiv.1903.00300,
title = {A bound for crystallographic arrangements},
author = {Michael Cuntz},
journal= {arXiv preprint arXiv:1903.00300},
year = {2019}
}
Comments
15 pages, 4 figures