##
**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 \lambda_{1}\sqrt{n}, where\lambda_{1} is a small constant. Here we study the case a \geq \lambda_{2}\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

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag