Elsevier

European Journal of Combinatorics

Volume 50, November 2015, Pages 30-37
European Journal of Combinatorics

Bijections between affine hyperplane arrangements and valued graphs

Dedicated to Michel Las Vergnas
https://doi.org/10.1016/j.ejc.2015.04.003Get rights and content
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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.

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