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Concerning periodicity in the asymptotic behaviour of partition functions

Published online by Cambridge University Press:  09 April 2009

P. Erdös  and
B. Richmond
P. Erdös
Affiliation:
University of Waterloo University Avenue, Waterloo Ontario, Canada
B. Richmond
Affiliation:
University of Waterloo University Avenue, Waterloo Ontario, Canada
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Abstract

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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 (aν = rν) there is a periodic component in the asymptotic behaviour of PA(n). We show by example that this may happen for sequences that satisfy aν ν 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.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 4 , June 1976 , pp. 447 - 456
Copyright
Copyright © Australian Mathematical Society 1976

References

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