Journal of Integer Sequences, Vol. 14 (2011), Article 11.4.1

Recurrence Relations and Two-Dimensional Set Partitions

Toufik Mansour
Department of Mathematics
University of Haifa
31905 Haifa, Israel

Augustine Munagi
John Knopfmacher Centre for Applicable Analysis and Number Theory
School of Mathematics
University of the Witwatersrand
Johannesburg, South Africa

Mark Shattuck
Department of Mathematics
University of Tennessee
Knoxville, TN 37996


In this paper, we consider a two-dimensional model for finite set partitions which arises in conjunction with a special case of a general non-linear recurrence. We investigate properties of some of the related counting sequences, including recurrences and generating functions. In particular, we obtain, by combinatorial arguments, some formulas relating these sequences to the Stirling numbers of the first kind. Specializing these arguments yields bijective proofs of some recent identities of Gould and Quaintance involving the Bell numbers, which were established using algebraic methods.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequences A000110 A000258 A008275 A008277.)

Received November 4 2010; revised version received March 14 2011. Published in Journal of Integer Sequences, March 26 2011.

Return to Journal of Integer Sequences home page