Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  727.11038
Autor:  Erdös, Paul; Nicolas, J.L.; Sárközy, A.
Title:  On the number of partitions of n without a given subsum. II. (In English)
Source:  Analytic number theory, Proc. Conf. in Honor of Paul T. Bateman, Urbana/IL (USA) 1989, Prog. Math. 85, 205-234 (1990).
Review:  [For the entire collection see Zbl 711.00008.]
Author's abstract: Let R(n,a) denote the number of unrestricted partitions of n whose subsums are all different of a, and Q(n,a) the number of unequal partitions (i.e. each part is allowed to occur at most once) with the same property. In a preceding paper [cf. Discrete Math. 75, 155-166 (1989; Zbl 673.05007)], we considered R(n,a) and Q(n,a) for a \leq \lambda1\sqrt{n}, where\lambda1 is a small constant. Here we study the case a \geq \lambda2\sqrt{n}. The behaviour of these quantities depends on the size of a, but also on the size of s(a), the smallest positive integer which does not divide a.
Reviewer:  B.Garrison (San Diego)
Classif.:  * 11P81 Elementary theory of partitions
                   05A17 Partitions of integres (combinatorics)
Keywords:  unrestricted partitions; unequal partitions
Citations:  Zbl 711.00008; Zbl 673.05007

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