A Combinatorial Bijection between Ordered Trees and Lattice Paths

L. Rocha, E. V. Pereira Spreafico


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+x^2)^n. Moreover, using a combinatorial interpretation of Catalan numbers, we establish a new set of ordered trees counted by a new sequence.


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

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DOI: https://doi.org/10.5540/tcam.2023.024.03.00427

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