The Combinatorics of Directed Planar Trees
Combinatorics
2017-04-20 v1 Geometric Topology
Quantum Algebra
Abstract
We give a geometric realization of the polyhedra governed by the structure of associative algebras with co-inner products, or more precisely, governed by directed planar trees. Our explicit realization of these polyhedra, which include the associahedra in a special case, shows in particular that these polyhedra are homeomorphic to balls. We also calculate the number of vertices of the lowest generalized associahedra, giving appropriate generalizations of the Catalan numbers.
Keywords
Cite
@article{arxiv.1704.05557,
title = {The Combinatorics of Directed Planar Trees},
author = {Kate Poirier and Thomas Tradler},
journal= {arXiv preprint arXiv:1704.05557},
year = {2017}
}
Comments
30 pages, 21 figures