A Combinatorial Bijection between Ordered Trees and Lattice Paths - Rocha, L.; Spreafico, E. V. Pereira (Trends in Computational and Applied Mathematics, 2023)
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.