Free hyperplane arrangements associated to labeled rooted trees

Details Free hyperplane arrangements associated to labeled rooted trees Free hyperplane arrangements associated to labeled rooted trees

2003-01-31

arxiv.org/abs/math/0301372v2

Mathematics

Combinatorics

16 pages, 3 figures, additional material on the topology of the complement and references added on supersolvable lattices and

Scientific paper

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.

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