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Constant Time Generation of Integer Partitions Katsuhisa YAMANAKA Shin-ichiro KAWANO Yosuke KIKUCHI Shin-ichi NAKANO Publication 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) Category: Keyword: algorithm, generation, integer partition, the family tree, Full Text: PDF(273.4KB)>>
Summary: 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. | ||||||||||
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