Bijections between affine hyperplane arrangements and valued graphs
classification
🧮 math.CO
keywords
arrangementsbijectivegraphshyperplaneproofssomeaffinearrangement
read the original 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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