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1991•Journal of Combinatorial Theory Series AOpen access

p, q-Stirling numbers and set partition statistics

Michelle L. Wachs, Dennis E. White

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Abstract

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.

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What this paper is about

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.

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Available abstract

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.

Key concepts: Bijection, injection and surjection, Stirling numbers of the second kind, Stirling number, Generating function, Mathematics, Stirling numbers of the first kind, Stirling engine, Combinatorics

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