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Mathematical Citation Quotient (MCQ) 2017: 0.20

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On a Partition Problem of Canfield and Wilf

Željka Ljujić / Melvyn B. Nathanson
Published Online: 2012-11-30 | DOI: https://doi.org/10.1515/integers-2012-0041


Let A and M be nonempty sets of positive integers. A partition of the positive integer n with parts in A and multiplicities in M is a representation of n in the form where for all , and for only finitely many a. Denote by the number of partitions of n with parts in A and multiplicities in M. It is proved that there exist infinite sets A and M of positive integers whose partition function has weakly superpolynomial but not superpolynomial growth. The counting function of the set A is . It is also proved that must have at least weakly superpolynomial growth if M is infinite and .

Keywords: Partitions; Representation Functions; Additive Number Theory

About the article

Received: 2011-05-30

Revised: 2012-04-18

Accepted: 2012-06-30

Published Online: 2012-11-30

Published in Print: 2012-12-01

Citation Information: Integers, Volume 12, Issue 6, Pages 1279–1286, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integers-2012-0041.

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© 2012 by Walter de Gruyter Berlin Boston.Get Permission

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