Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  403.10004
Autor:  Erdös, Paul; Loxton, J.H.
Title:  Some problems in partitio numerorum. (In English)
Source:  J. Aust. Math. Soc., Ser. A 27, 319-331 (1979).
Review:  The paper investigates asymptotic results for certain partition problems in which the parts are restricted by divisibility conditions. For example, let p(n) be the number of partitions n = a1+...+ak into positive integers with a1|a2|...|ak and let q(n) be the number of these partitions with distinct parts. We find that p(n) behaves like the binary partition function which counts partitions into powers of 2 and can be estimated precisely. The behaviour of q(n) is less amenable to analysis and leads to questions on the distribution of primes in sequences of the shape 2am+1.
Classif.:  * 11P81 Elementary theory of partitions
                   11N05 Distribution of primes
                   00A07 Problem books
Keywords:  partition; divisibility conditions; distribution of primes
Index Words:  Problems

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