On Postnikov's hook length formula for binary trees

We present a combinatorial proof of Postnikov's hook length formula for binary trees. c 2007 Elsevier Ltd. All rights reserved. Let [n] = {1, 2, . . . , n}. It is well known that the number of labeled trees on [n] equals nn-2, and the number of rooted trees on [n] equals nn-1 [5,8]. Recently, Postnikov derived an identity on binary trees and asked for a combinatorial proof [6]. We adopt the terminology of Postnikov [6]. Given a binary tree T and a vertex v of T , we use h(v) to denote the hook length of v, namely, the number of descendants of v (including v itself). Postnikov's hook length formula for binary trees reads as follows.

• Type: Journal
• Year: 2008
• Where: EJC
• Authors: William Y. C. Chen, Laura L. M. Yang
• Keywords: Binary Trees, Combinatorial Proof, EJC 2007, EJC 2008, Hook Length Formula, Information Technology