##
**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 326.10042

**Autor: ** Erdös, Paul; Richmond, B.

**Title: ** Concerning periodicity in the asymptotic behaviour of partition functions. (In English)

**Source: ** J. Aust. Math. Soc., Ser. A 21, 447-456 (1976).

**Review: ** Let P_{A}(n) denote the number of partitions of n into summands chosen from the set A = **{**a_{0},a_{1}, ... **}**. De Bruijn has shown that in Mahler's partition problem (a_{\nu} = r^{\nu}) there is a periodic component in the asymptotic behaviour of P_{A}(n). We show by example that this may happen for sequences that satisfy a_{\nu} ~ \nu 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.

**Classif.: ** * 11P81 Elementary theory of partitions

11P81 Elementary theory of partitions

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag