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IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 2007 E90-A(5):888-895; doi:10.1093/ietfec/e90-a.5.888
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Copyright © 2007 The Institute of Electronics, Information and Communication Engineers

Special Section on Discrete Mathematics and Its Applications -- Papers

Constant Time Generation of Integer Partitions

Katsuhisa YAMANAKA1, Shin-ichiro KAWANO1, Yosuke KIKUCHI2 and Shin-ichi NAKANO1

1 The authors are with the Department of Computer Science, Gunma University, Kiryu-shi, 376–8515 Japan. E-mail: yamanaka{at}msc.cs.gunma-u.ac.jp, E-mail: kawano{at}msc.cs.gunma-u.ac.jp, E-mail: nakano{at}msc.cs.gunma-u.ac.jp, 2 The author is with the Tsuyama National College of Technology, Tsuyama-shi, 708–8509 Japan. E-mail: kikuchi{at}tsuyama-ct.ac.jp


  Abstract

In this paper we give a simple algorithm to generate all partitions of a positive integer n. The problem is one of the basic problems in combinatorics, and has been extensively studied for a long time. Our algorithm generates each partition of a given integer in constant time for each without repetition, while best known algorithm generates each partition in constant time on "average." Also, we propose some algorithms to generate all partitions of an integer with some additional property in constant time.

Key Words: algorithm, generation, integer partition, the family tree

Manuscript received August 18, 2006. Manuscript revised November 10, 2006. Final manuscript received December 25, 2006.


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