A bijection on ordered trees and its consequences
A bijection is introduced in the set of all ordered trees having \(n\) edges from which one derives that, for each positive integer \(q\), the number of nodes of degree \(q\) and the number of odd-level nodes of degree \(q-1\) are equidistributed. Since ordered trees with no nodes of degree higher than 2 are enumerated by the Motzkin numbers, it follows that also the ordered trees with no branching nodes at odd levels are enumerated by the Motzkin numbers. This is a recent result of \textit{A. Kuznetsov, I. Pak} and \textit{A. Postnikov} [J. Comb. Theory, Ser. A 76, No. 1, 145-147 (1996; Zbl 0860.05003)], which has inspired the author of this note.
scientific article; zbMATH DE number 1443256