Left ternary trees and non-separable rooted planar maps

In this paper, we illustrate a bijective proof of the enumerative formula r egarding non-separable rooted planar maps NY, by means of a class L of cert ain ternary trees (called left trees). Our first step consists in determini ng the left trees' combinatorial enumeration according to the number of the ir internal nodes. We then establish a bijection between the left trees hav ing n internal nodes and the non-separable rooted planar maps with n + 1 ed ges. We wish to point out that in the bijection, L and NY have many corresp onding parameters to each other. (C) 2000 Elsevier Science B.V. All rights reserved.