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 = (an) and x = (xn) be sequences of non-negative integers. Let a.x = sum anxn. 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 an increases unboundedly and xn is positive and decreases to zero, then the set of numbers in question is the interval [a.x,oo] if and only if an+1/an 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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