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The largest (k,ℓ)-sum-free subsets.
- Source :
-
Transactions of the American Mathematical Society . Jul2021, Vol. 374 Issue 7, p5163-5189. 27p. - Publication Year :
- 2021
-
Abstract
- Let M(2,1)(N) be the infimum of the largest sum-free subset of any set of N positive integers. An old conjecture in additive combinatorics asserts that there is a constant c = c(2,1) and a function ω (N) → ∞ as N → ∞, such that cN + ω (N) < M(2,1)(N) < (c + o(1))N. The constant c(2,1) is determined by Eberhard, Green, and Manners, while the existence of ω (N) is still wide open. In this paper, we study the analogous conjecture on (k,ℓ)-sum-free sets and restricted (k,ℓ)-sum-free sets. We determine the constant c(k,ℓ) for every (k,ℓ)-sum-free sets, and confirm the conjecture for infinitely many (k,ℓ). [ABSTRACT FROM AUTHOR]
- Subjects :
- *LOGICAL prediction
*INTEGERS
*COMBINATORICS
Subjects
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 374
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 150746344
- Full Text :
- https://doi.org/10.1090/tran/8385