We give bijections on restricted growth functions and rook placements on stairstep Ferrers boards to show that the q-Stirling numbers of the second kind, described by Gould, arise as generating functions for various statistics on set partitions. We also describe a two-variable, p, q-Stirling number which is the generating function for the joint distribution of pairs of statistics.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics