Concerning periodicity in the asymptotic behaviour of partition functions

P. Erdős, B. Richmond

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Let PA(n) denote the number of partitions of n into summands chosen from the set A ={a1, a2,···}. De Bruijn has shown that in Mahler’s partition problem (av = rv) there is a periodic component in the asymptotic behaviour of PA(n). We show by example that this may happen for sequences that satisfy av ~ v and consider an analogous phenomena for partitions into primes. We then consider corresponding results for partitions into distinct summands. Finally we obtain some weaker results using elementary methods.

Original languageEnglish
Pages (from-to)447-456
Number of pages10
JournalJournal of the Australian Mathematical Society
Volume21
Issue number4
DOIs
Publication statusPublished - 1976

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Partition Function
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Cite this

Concerning periodicity in the asymptotic behaviour of partition functions. / Erdős, P.; Richmond, B.

In: Journal of the Australian Mathematical Society, Vol. 21, No. 4, 1976, p. 447-456.

Research output: Contribution to journalArticle

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