On arrangements of hyperplanes from connected subgraphs
Combinatorics
2022-09-21 v2
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.
Keywords
Cite
@article{arxiv.2208.09251,
title = {On arrangements of hyperplanes from connected subgraphs},
author = {Michael Cuntz and Lukas Kühne},
journal= {arXiv preprint arXiv:2208.09251},
year = {2022}
}
Comments
22 pages, 7 figures, minor edits