This work is based on the paper Deformations of Coxeter hyperplane arrangements by Stanley and Postnikov from 2000s and other papers from the beginning of the 2000s. We extend the connections between the Linial (resp. Shi, Braid, Catalan) arrangements and alternating (resp. Cayley, increasing, labeled binary) trees to connections to general families of arrangements and colored trees. We use a mix of gain-graph theory, NBC sets, bijections and generating functions.
This is joint work with David Forge (Orsay) and Anne Micheli (Paris 7).