Purpose and Scope.

Riordan Arrays (RA) is a growing field that is both absorbing nutrients from, and continuing its contributions to, other fields.  We hope all conference participants will benefit from interacting with each other, particularly with RA people. During and after the conference, many new results could emerge when people working in related fields look at RA and RA people look at other fields.  An important aim of this symposium is to provide a venue for this interaction.

Another purpose of this symposium is to facilitate the exchange of ideas concerning the current trends in the theory and applications of Riordan Arrays and topics related to the study of Riordan Arrays.  Riordan arrays were introduced in 1991 by L. W. Shapiro, S. Getu, W. J. Woan, and L. Woodson with the aim of defining a class of infinite lower triangular arrays with properties analogous to those of Pascal’s triangle. In 1994, R. Sprugnoli pointed out the importance of these matrices for the computation of combinatorial sums. Riordan arrays have been an important and burgoening topic ever since their inception.  A few areas of study have been the algebraic structure of these matrices (the Riordan group), their relationship with the computation of combinatorial sums, and many combinatorial applications.

For this symposium, similar to the first two symposia, particular areas of interest include (but are not limited to) the algebraic structure of Riordan arrays, Riordan arrays and combinatorial sums, Sheffer matrices, Umbral Calculus, lattice paths, combinatorics of posets, lattices and words, and many other aspects of combinatorics and their relationships with other areas of mathematics, computer science, physics, biology, and other fields.