Technical Report: DCC-2004-07

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, 4150-180 Porto, Portugal
Phone: 351 226.078.830, Fax: 351 226.003.654
E-mail: {nam, rvr} at

August 2004


We present a family of regular languages representing partitions of a set Nn={1,...,n} in less or equal c parts. We determine explicit formulas for the density of those languages and their relationship with well known integer sequences involving Stirling numbers of second kind. We also determine their limit frequency. This work was motivated by computational representations of the configurations of some numerical games.