Résumé : Historically, there exist two versions of the Riordan array concept. The older one (better known as recursive matrix and introduced by Barnabei, Brini and Nicoletti) consists of bi-infinite matrices, deals with formal Laurent series and has been mainly used to study algebraic properties of such matrices. The more recent version consists of infinite, lower triangular arrays, deals with formal power series and has been used to study combinatorial problems. The name Riordan arrays has been coined in 1991 by Shapiro, Getu, Woan and Woodson with the aim of defining a class of infinite lower triangular arrays with properties analogous to those of the Pascal triangle. This concept has been successively studied by Sprugnoli in the context of the computation of combinatorial sums. Some other important aspects of the theory have been studied later by Merlini, Sprugnoli and Verri and the literature about Riordan arrays is vast and still growing. After describing the classical properties about this concept, in this talk we present some recent results concerning Riordan arrays related to binary words avoiding a pattern p and show that every Riordan array induces two characteristic combinatorial identities in three parameters n, k, m in Z which are valid in the bi-infinite realm of recursive matrices.
|Dernière modification : Friday 09 December 2011||Contact : Cyril.Banderier at lipn.univ-paris13.fr|