# Dyck path binary tree bijection

Parity reversing involutions on plane trees and 2-Motzkin paths. An internal vertex v is called pure if its children are all internal vertices or all leaves, otherwise it is called mixed. Let G x, t be the ordinary generating function of compatible ternary trees, where x and t mark the number of internal vertices and right leaves, respectively.

Stanley, Catalan Addendumversion of 30 April The set of p-ary trees with n internal vertices is counted by the generalized Catalan number Stanley, An internal vertex v dyck path binary tree bijection called pure if its children are all internal vertices or all leaves, otherwise it is called mixed. Recall that the plane trees with n edges and k leaves obey the Narayana distribution Dershowitz and Zaks, ; Deutsch,i. Information Technology Journal,

A leaf is referred as a right leaf if it is the rightmost child of some internal vertex. There are two cases according to the youngest child, say w, of v. How to cite this article: Now the generalization of Theorem 2 is given.

This gives a new combinatorial interpretation of Motzkin sequence. By convention, a 2-ary tree is called a complete binary tree and the Catalan sequence c 2 n is denoted by c n. Denoting CB e n resp. It dyck path binary tree bijection also known as order-p Fuss-Catalan number Fomin and Reading,

Retrieved from " https: Some q-analogues of the Schroder numbers arising from combinatorial statistics on lattice paths. This study investigates the number of right leaves in p-ary trees.

Explicitly, given such a compatible ternary tree T with root r, suppose T 1 and Dyck path binary tree bijection 2 is the first and second subtree of r respectively. The structure of p-ary tree is a generalization of the structure of binary tree such that each internal vertex has p children. The binary tree is an important structure in computer science. Substituting p n,k by the Narayana number in the above equation and applying Cauchy Residue Theorem, it gives:. Personal tools Log in Request account.