Constant Time Generation of Integer Partitions

Katsuhisa YAMANAKA  Shin-ichiro KAWANO  Yosuke KIKUCHI  Shin-ichi NAKANO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E90-A   No.5   pp.888-895
Publication Date: 2007/05/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e90-a.5.888
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
algorithm,  generation,  integer partition,  the family tree,  

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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.