Subdivision des nombres de Narayana suivant deux paramètres supplémentaires. (Subdivision of Narayana numbers following two supplementary parameters) (Q1104327)

In any n-bridge, apart from the parameter p (total number of jumps or of landings), which is known to be distributed according to the Narayana law, the paper introduces two additional parameters i and j, respectively defined as the number of long jumps and the number of long non-final landings (long means consisting of at least two steps). It is shown that the number of n-bridges with prescribed p, i and j is a remarkably simple monomial function D(n,p,i,j). The proof makes use of the auxiliary concept of `pseudo-bridge' and is mainly combinatorial but also partly analytical.