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**Zentralblatt MATH**

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

**Zbl.No: ** 539.40001

**Autor: ** Erdös, Paul; Weiss, Gary

**Title: ** Dot product rearrangements. (In English)

**Source: ** Int. J. Math. Math. Sci. 6, 409-418 (1983).

**Review: ** Let a = (a_{n}) and x = (x_{n}) be sequences of non-negative integers. Let a.x = **sum** a_{n}x_{n}. Letting x_{\pi} denote a permutation of the sequence x, this paper investigates which subsets of **R** can be realised as a.x_{\pi}. The main result is that if a_{n} increases unboundedly and x_{n} is positive and decreases to zero, then the set of numbers in question is the interval [a.x,oo] if and only if a_{n+1}/a_{n} is uniformly bounded.

**Reviewer: ** K.E.Hirst

**Classif.: ** * 40A05 Convergence of series and sequences

**Keywords: ** dot product, series rearrangements; conditional convergence

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