Abstract
We study lattice paths by combinatorial methods on the positive lattice. We give some identity that produces the functional equations and generating functions to counting the lattice paths on or below the main diagonal. Also, we consider the subdiagonal lattice paths in relation to lower triangular arrays. This presents a Riordan array in conjunction with the columns of the matrix of the coefficients of certain formal power series by implying an infinite lower triangular matrix \( F=(f_{x,y})_{x,y\geqslant 0} \). We derive new combinatorial interpretations in terms of restricted lattice paths for some Riordan arrays.
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The work is supported by the Mathematical Center in Akademgorodok under the agreement no. 075–15–2022–281 with the Ministry of Science and Higher Education of the Russian Federation.
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Chandragiri, S. Riordan Arrays and Difference Equations of Subdiagonal Lattice Paths. Sib Math J 65, 411–425 (2024). https://doi.org/10.1134/S0037446624020149
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DOI: https://doi.org/10.1134/S0037446624020149