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

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, Schroder paths, RNA secondary structures, noncrossing partitions, Fine paths, and Davenport-Schinzel sequences.

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