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A bijection between 2-triangulations and pairs of non-crossing Dyck paths

Sergi Elizalde
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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.

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Sergi Elizalde. 2006-10-06. A bijection between 2-triangulations and pairs of non-crossing Dyck paths. https://arxiv.org/abs/math/0610235

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