Bijections between affine hyperplane arrangements and valued graphs
Combinatorics
2014-08-26 v2
Abstract
We show new bijective proofs of previously known formulas for the number of regions of some deformations of the braid arrangement, by means of a bijection between the no-broken-circuit sets of the corresponding integral gain graphs and some kinds of labelled binary trees. This leads to new bijective proofs for the Shi, Catalan, and similar hyperplane arrangements.
Cite
@article{arxiv.1403.2573,
title = {Bijections between affine hyperplane arrangements and valued graphs},
author = {Sylvie Corteel and David Forge and Véronique Ventos},
journal= {arXiv preprint arXiv:1403.2573},
year = {2014}
}
Comments
9 pages, 2 figures