Geodesic
On the density of languages representing finite set partitions
Journal of integer sequences, Tome 8 (2005) no. 2
We present a family of regular languages representing partitions of a set of $n$ elements in less or equal $c$ parts. The density of those languages is given by partial sums of Stirling numbers of second kind for which we obtain explicit formulas. We also determine the limit frequency of those languages. This work was motivated by computational representations of the configurations of some numerical games.
Classification : 05A15, 05A18, 11B73, 68Q45
Keywords: partions of sets, Stirling numbers, regular languages, enumeration (Concerned with sequences A000110 A000225 A00705 
@article{JIS_2005__8_2_a3,
     author = {Moreira,  Nelma and Reis,  Rog\'erio},
     title = {On the density of languages representing finite set partitions},
     journal = {Journal of integer sequences},
     year = {2005},
     volume = {8},
     number = {2},
     zbl = {1064.05017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2005__8_2_a3/}
}
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Moreira,  Nelma; Reis,  Rogério. On the density of languages representing finite set partitions. Journal of integer sequences, Tome 8 (2005) no. 2. http://geodesic.mathdoc.fr/item/JIS_2005__8_2_a3/