A note on Abel polynomials and rooted labeled forests
A special case of the Abel polynomials counts rooted labeled forests. This interpretation is used to obtain a combinatorial proof of the formula expressing x^n as a sum of these polynomials.
On the combinatorics of Riordan arrays and Sheffer polynomials: monoids, operads and monops
We introduce a new algebraic construction, {\em monop}, that combines monoids (with respect to the product of species), and operads (monoids with respect to the substitution of species) in the same algebraic structure. By the use of properties of cancellative set-monops we construct a family of partially ordered sets whose prototypical examples are the Dowling lattices. They generalize the partition posets associated to a cancellative operad, and the subset posets associated to a cancellative monoid. Their generalized Withney numbers of the first and second kind are the entries of a Riordan matrix and its inverse. Equivalently, they are the connecting coefficients of two umbral inverse Sheffer sequences with the family of powers $\{x^n\}_{n=0}^{\infty}$. We study algebraic monops, their associated algebras and the free monop-algebras, as part of a program in progress to develop a theory of Koszul duality for monops.
Réarrangements de fonctions et dénombrement
Resume On donne l'enonce d'un theoreme sur les rearrangements d'applications d'un ensemble fini dans lui-meme, qui generalise un resultat connu sur les permutations, et qui permet de retrouver le denombrement des classes d'applications ultimement idempotentes et indecomposables, ainsi que celui des arbres de n sommets et des graphes connexes de n aretes et n sommets.