30/06/2015, 14:00 — 15:00 — Sala P4.35, Pavilhão de Matemática
Ângela Mestre, CEAFEL, Universidade de Lisboa
Counting noncrossing partitions via Catalan triangles
We introduce a family of Riordan arrays which depend on four parameters. The entries of these generalized Catalan triangles are homogeneous polynomials in two variables which interpolate between the ballot numbers and the binomial coefficients. We show that the generalized Pascal triangle as well as the Catalan arrays introduced by Shapiro, Aigner, Radoux, He, or Yang are all special members of this wide family of parameterized Catalan triangles. Moreover, as an application, we deal with the enumeration of noncrossing partitions according to the following statistical parameters: the size of the partition set, the number of blocks, the number of singletons, and the number of the parts in which they can be decomposed.
Our results point out new enumerative properties of classical combinatorial objects such as the Catalan numbers, the ballot numbers, the Narayana numbers, or the Catalan triangle of Shapiro.
This is joint work with J. Agapito, P. Petrullo, and M. M. Torres.
Ver também
ceafel.pdf
