A bijection between 2-triangulations and pairs of non-crossing Dyck paths
Combinatorics
2007-05-23 v1
Abstract
A k-triangulation of a convex polygon is a maximal set of diagonals so that no k+1 of them mutually cross in their interiors. We present a bijection between 2-triangulations of a convex n-gon and pairs of non-crossing Dyck paths of length 2(n-4). This solves the problem of finding a bijective proof of a result of Jonsson for the case k=2. We obtain the bijection by constructing isomorphic generating trees for the sets of 2-triangulations and pairs of non-crossing Dyck paths.
Cite
@article{arxiv.math/0610235,
title = {A bijection between 2-triangulations and pairs of non-crossing Dyck paths},
author = {Sergi Elizalde},
journal= {arXiv preprint arXiv:math/0610235},
year = {2007}
}
Comments
17 pages, 12 figures