Free hyperplane arrangements associated to labeled rooted trees
نویسنده
چکیده
To each labeled rooted tree is associated 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.
منابع مشابه
The Hopf Algebra of Rooted Trees, Free Lie Algebras, and Lie Series
We present an approach that allows performing computations related to the Baker-Campbell-Haussdorff (BCH) formula and its generalizations in an arbitrary Hall basis, using labeled rooted trees. In particular, we provide explicit formulas (given in terms of the structure of certain labeled rooted trees) of the continuous BCH formula. We develop a rewriting algorithm (based on labeled rooted tree...
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