Geodesic
Recurrence relations and two-dimensional set partitions
Journal of integer sequences, Tome 14 (2011) no. 4
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.
Classification : 05A18, 05A19, 05A15
Keywords: set partition, generating function, recurrence relation, combinatorial proof 
@article{JIS_2011__14_4_a1,
     author = {Mansour,  Toufik and Munagi,  Augustine and Shattuck,  Mark},
     title = {Recurrence relations and two-dimensional set partitions},
     journal = {Journal of integer sequences},
     year = {2011},
     volume = {14},
     number = {4},
     zbl = {1217.05037},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_4_a1/}
}
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Mansour,  Toufik; Munagi,  Augustine; Shattuck,  Mark. Recurrence relations and two-dimensional set partitions. Journal of integer sequences, Tome 14 (2011) no. 4. http://geodesic.mathdoc.fr/item/JIS_2011__14_4_a1/