Let N denote the set of positive integers. The asymptotic density of the set /n, if this limit exists. Let AD denote the set of all sets of positive integers that have asymptotic density, and let S N denote the set of all permutations of the positive integers N. The group L consists of all permutat
โฆ LIBER โฆ
Asymptotic density of certain sets of natural numbers
โ Scribed by E. I. Shustin
- Publisher
- Springer US
- Year
- 1985
- Tongue
- English
- Weight
- 310 KB
- Volume
- 29
- Category
- Article
- ISSN
- 1573-8795
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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