Concerning periodicity in the asymptotic behaviour of partition functions
- 1 March 1976
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 21 (4) , 447-456
- https://doi.org/10.1017/s1446788700019285
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 (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.Keywords
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