Concerning periodicity in the asymptotic behaviour of partition functions

P. Erdős, B. Richmond

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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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ASJC Scopus subject areas

  • Mathematics(all)

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