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The largest $(k,\ell )$-sum-free subsets

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 set...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1090/tran/8385

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
ORCID:
0000-0002-9954-7182
Publisher:
American Mathematical Society
Journal:
Transactions of the American Mathematical Society More from this journal
Volume:
374
Issue:
7
Pages:
5163-5189
Publication date:
2021-04-27
Acceptance date:
2021-01-09
DOI:
EISSN:
1088-6850
ISSN:
0002-9947
Language:
English
Keywords:
Pubs id:
1207666
Local pid:
pubs:1207666
Deposit date:
2021-11-09

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