Constant Time Generation of Set Partitions

Authors:
Shin-Ichiro Kawano;Shin-Ichi Nakano
Affiliations:
The authors are with the Department of Computer Science, Gunma University, Kiryu-shi, 376-8515 Japan. E-mail: kawano@msc.cs.gunma-u.ac.jp, E-mail: nakano@msc.cs.gunma-u.ac.jp;The authors are with the Department of Computer Science, Gunma University, Kiryu-shi, 376-8515 Japan. E-mail: kawano@msc.cs.gunma-u.ac.jp, E-mail: nakano@msc.cs.gunma-u.ac.jp
Venue:
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Year:
2005

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Abstract

In this paper we give a simple algorithm to generate all partitions of {1, 2, ..., n} into k non-empty subsets. The number of such partitions is known as the Stirling number of the second kind. The algorithm generates each partition in constant time without repetition. By choosing k = 1, 2, ..., n we can also generate all partitions of {1, 2, ..., n} into subsets. The number of such partitions is known as the Bell number.