Journal of Integer Sequences, Vol. 20 (2017), Article 17.4.7

Constructing Pseudo-Involutions in the Riordan Group

Dev Phulara
National Security Agency
Fort Meade, MD 20755

Louis Shapiro
Howard University
Washington, DC 20059


Involutions and pseudo-involutions in the Riordan group are interesting because of their numerous applications. In this paper we study involutions using sequence characterizations of the Riordan arrays. For a given B-sequence we find the unique function f(z) such that the array (g(z), f (z)) is a pseudo-involution. As a combinatorial application, we find the interpretation of each entry in the Bell array (g(z),f(z)) with a given B-sequence.

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(Concerned with sequences A000245 A004148 A023431 A091561 A091565 A102893 A105633 A187256 A233658.)

Received November 11 2016; revised versions received February 2 2017; February 12 2017. Published in Journal of Integer Sequences, February 18 2017.

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