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**Zentralblatt MATH**

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

**Zbl.No: ** 483.10014

**Autor: ** Erdös, Paul; Richmond, B.

**Title: ** Partitions into summands of the form [malpha]. (In English)

**Source: ** Numerical mathematics and computing, Proc. 7th Manitoba Conf., Winnipeg/Can. 1977, Congr. Numerantium 20, 371-377 (1978).

**Review: ** [For the entire collection see Zbl 465.00021.]

Asymptotic estimates for the number of partitions of the integer n into summandschosen from an arithmetic progression have been derived by several authors. In this note we investigate a natural extension which has not previously appeared in the literature. We study the asymptotic behaviour of the numbers p_{\alpha}(n) and q_{\alpha}(n). The number of partitions of n into summands and distinct summands, respectively, chosen from the sequence [m\alpha],m = 1,2,... where \alpha > 1 is an irrational number and [x] denotes the largest integer \leq x. If \gamma = \alpha-[\alpha] then for almost all \gamma in (0,1) in the Lesbesgue sense we obtain asymptotic formulae for p_{\alpha}(n) and q_{\alpha}(n).

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

**Keywords: ** asymptotic estimates; number of partitions; arithmetic progression

**Citations: ** Zbl.465.00021

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