Publications of (and about) Paul Erdös
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
© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag