Pseudo-involutions in the Riordan group and Chebyshev polynomials

2025/02/19 by Burstein, Alexander, Shapiro, Louis W. · 1 citation
#05A15 (Primary) 05A05 #05A19 #11B83 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.13673

Abstract

Generalizing the results in our previous paper, we consider pseudo-involutions in the Riordan group where the generating function g for the first column of a Riordan array satisfies a functional equation of certain types involving a polynomial. For those types of equations, we find the pseudo-involutory companion of g. We also develop a general method for finding B-functions of Riordan pseudo-involutions in the cases we consider, and show that these B-functions involve Chebyshev polynomials. We apply our method for several families of Riordan arrays, obtaining new results and deriving known results more efficiently.

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