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arXiv · 1403.2573

Bijections between affine hyperplane arrangements and valued graphs

Sylvie Corteel·David Forge·Véronique Ventos
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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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Sylvie Corteel, David Forge, Véronique Ventos. 2014-08-23. Bijections between affine hyperplane arrangements and valued graphs. https://arxiv.org/abs/1403.2573

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