Free hyperplane arrangements associated to labeled rooted trees
Abstract
Description
Each labeled rooted tree is associated with a hyperplane arrangement, which is free with exponents given by the depths of the vertices of this tree. The intersection lattices of these arrangements are described through posets of forests. These posets are used to define coalgebras, whose dual algebras are shown to have a simple presentation by generators and relations.
16 pages, 3 figures, additional material on the topology of the complement and references added on supersolvable lattices and graphical arrangements
16 pages, 3 figures, additional material on the topology of the complement and references added on supersolvable lattices and graphical arrangements