Journal of Integer Sequences, Vol. 8 (2005), Article 05.3.7

On Some (Pseudo) Involutions in the Riordan Group

Naiomi T. Cameron
Department of Mathematics
Occidental College
Los Angeles, CA 90041
USA

Asamoah Nkwanta
Department of Mathematics
Morgan State University
Baltimore, MD 21251
USA

Abstract: In this paper, we address a question posed by L. Shapiro regarding algebraic and/or combinatorial characterizations of the elements of order 2 in the Riordan group. We present two classes of combinatorial matrices having pseudo-order 2. In one class, we find generalizations of Pascal's triangle and use some special cases to discover and prove interesting identities. In the other class, we find generalizations of Nkwanta's RNA triangle and show that they are pseudo-involutions.

(Concerned with sequences A000108 A000225 A001003 A001006 A001519 A001906 A004148 A007318 A038231 A038255 A039598 A053122 A097724 A110438 A110439 A110440 and A110441 .)

Received June 17 2005; revised version received August 18 2005. Published in Journal of Integer Sequences August 23 2005.