The (l,r)-Stirling numbers: A combinatorial approach

Abstract

This work deals with a new generalization of r-Stirling numbers using l-tuple of permutations and partitions called (l,r)-Stirling numbers of both kinds. We study various properties of these numbers using combinatorial interpretations and symmetric functions. Also, we give a limit representation of the multiple zeta function using (l,r)-Stirling of the first kind.