A bijection between ordered trees and 2-Motzkin paths and its many consequences

Authors:
Emeric Deutsch;Louis W. Shapiro
Affiliations:
Department of Mathematics, Polytechnic University, Brooklyn, NY;Howard University, Washington, DC
Venue:
Discrete Mathematics
Year:
2002

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Abstract

A new bijection between ordered trees and 2-Motzkin paths is presented, together with its numerous consequences regarding ordered trees as well as other combinatorial structures such as Dyck paths, bushes, {0, 1, 2}-trees, Schröder paths, RNA secondary structures, noncrossing partitions, Fine paths, and Davenport-Schinzel sequences.