On arrangements of hyperplanes from connected subgraphs

authored by

Michael Cuntz, Lukas Kühne

Abstract

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, simplicial, factored, or supersolvable. In particular, such an arrangement is free if and only if the graph is a cycle, a path, an almost path, or a path with a triangle attached to it.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

Bielefeld University

Type

Preprint

No. of pages

21

Publication date

19.08.2022

Publication status

E-pub ahead of print

Electronic version(s)

https://arxiv.org/abs/2208.09251 (Access: Open)