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Articles • Trends Comput. Appl. Math. 24 (3) • Jul-Sep 2023 • https://doi.org/10.5540/tcam.2023.024.03.00427   copy

A Combinatorial Bijection between Ordered Trees and Lattice Paths

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

This work presents a combinatorial bijection between the set of lattice paths and the set of ordered trees, both counted by the central coefficients of the expansion of the trinomial (1 + x + x2)n. Moreover, using a combinatorial interpretation of Catalan numbers, we establish a new set of ordered trees counted by a new sequence.

Keywords:
lattice paths; ordered trees; combinatorial identity; central trinomial coefficients

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