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Arithmetic progressions in sumsets

✍ Scribed by B. Green

Publisher: Springer
Year: 2002
Tongue: English
Weight: 174 KB
Volume: 12
Category: Article
ISSN: 1016-443X
DOI: 10.1007/s00039-002-8258-4

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~roughout this paper we use the following notatians: The cardinality of the finite set Y is denoted by ISI -.s& B8, . I s den&e finite or infinite sets of positive integers. If & is a finite or infinite set of positive integers, then S(d) denotes the set of the distinct positive integers n that can

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A set of real numbers a~ < a 2 <... < cl L is called a weakly arithmetic progression of length L, if there exist L consecutive intervals I i = [x i\\_ ~, xl), i = 1 ..... L, of equal length with a~El i. Here we consider conditions from which the existence of weakly arithmetic progressions can (resp.