On strongly reversible elements in the Riordan group

Abstract

An element of a group is called \emph{reversible} if it is conjugate to its inverse, and \emph{strongly reversible} if it can be expressed as a product of two involutions. We study strongly reversible elements in the Riordan group and its various important subgroups. We prove that not every reversible element in the Riordan group is strongly reversible, and we investigate products of reversible elements in the Riordan group.

arXiv commentFinal version, 8 pages. To appear in Linear and Multilinear Algebra. Revised title, strengthened introduction, and improved exposition throughout