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On the Number of Sum-Free Sets

โœ Scribed by Calkin, N. J.


Book ID
120092694
Publisher
Oxford University Press
Year
1990
Tongue
English
Weight
84 KB
Volume
22
Category
Article
ISSN
0024-6093

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๐Ÿ“œ SIMILAR VOLUMES


On Infinite Sum-free Sets of Natural Num
โœ Tomasz ล‚uczak; Tomasz Schoen ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 346 KB

A subset of the natural numbers is k-sum-free if it contains no solutions of the equation x 1 + } } } +x k = y, and strongly k-sum-free when it is l-sum-free for every l=2, ..., k. It is shown that every k-sum-free set with upper density larger than 1ร‚(k+1) is a subset of a periodic k-sum-free set a

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in this note we obtain new tower bounds for the Ramsey numbers R(5,S) and R(5,6). The methrld is based on computational results of partitioning the integers into sum-free sets. WC obtain R(S, 5) > 42 and R(5,6) 2 53.

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