Journal of Integer Sequences, Vol. 8 (2005), Article 05.2.8

On the Density of Languages Representing Finite Set Partitions

Nelma Moreira and Rogério Reis
DCC-FC & LIACC
Universidade do Porto
R. do Campo Alegre 823
4150 Porto
Portugal

Abstract: 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.

(Concerned with sequences A000110 A000225 A007051 A007581 A008277 A047926 A056272 A056273 A099262 A099263 A099265 A099266 .)

Received October 14 2004; revised version received April 17 2005. Published in Journal of Integer Sequences May 18 2005.