A Three-parameter Family Of Involutions In The Riordan Group Defined By Orthogonal Polynomials

2022/07/06 by Barry, Paul
#05A19 #11B83 #Combinatorics (math.CO) #FOS: Mathematics #Primary 05A15. Secondary 05A05

paper · doi:10.48550/arxiv.2207.02719

Abstract

We show how to define, for every Riordan group element (g(x), f(x)), an involution in the Riordan group. More generally, we show that for every pseudo-involution P in the Riordan group, we can define a new involution beginning with an arbitrary element (g(x), f(x)) in the Riordan group. We then use this result to show that certain two-parameter families of orthogonal polynomials defined by a Riordan array can lead to involutions in the Riordan group, and we give an explicit form of these involutions.

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