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

作者：Elizalde Sergi^*

来源：Journal of Combinatorial Theory - Series A, 2007, 114(8): 1481-1503.

DOI：10.1016/j.jcta.2007.03.002

• generalized triangulation
• dyck path
• bijection
• crossing

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 noncrossing 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.

• 出版日期2007-11