Regresar

Generalized ordered set partitions

Abstract:

In this paper, we consider ordered set partitions obtained by imposing conditions on the size of the lists, and such that the first r elements are in distinct blocks, respectively. We introduce a generalization of the Lah numbers. For this new combinatorial sequence we derive its exponential generating function, some recurrence relations, and combinatorial identi-ties. We prove and present results using combinatorial arguments, generating functions, the symbolic method and Riordan arrays. For some specific cases we provide a combinatorial interpretation for the inverse matrix of the generalized Lah numbers by means of two families of posets.