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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