Left ternary trees and non-separable rooted planar maps

In this paper, we illustrate a bijective proof of the enumerative formula regarding non-separable rooted planar maps NY, by means of a class L of certain ternary trees (called left trees). Our first step consists in determining the left trees' combinatorial enumeration according to the number of their internal nodes. We then establish a bijection between the left trees having n internal nodes and the non-separable rooted planar maps with n + 1 edges. We wish to point out that in the bijection, L and NY have many corresponding parameters to each other. (C) 2000 Elsevier Science B.V. All rights reserved.