A bijection on ordered trees and its consequences
type: Item
instance of: scholarly article
title: A bijection on ordered trees and its consequences
zbMATH Open document ID: 0943.05031
author: Emeric Deutsch
published in: Journal of Combinatorial Theory. Series A
publication date: 2000-08-28T00:00:00Z
review text: 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.
reviewed by: Lutz Volkmann
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 1443256
zbMATH Keywords: ordered trees
zbMATH Keywords: bijection
zbMATH Keywords: level of a node
zbMATH Keywords: Motzkin numbers
MaRDI profile type: Publication
full work available at URL: jcta.1999.3027
OpenAlex ID: W2030390773
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DOI: 10.1006/JCTA.1999.3027
description: scientific article; zbMATH DE number 1443256