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Long, Jason; Wagner, Adam Zsolt

doi:10.1016/j.ejc.2019.05.005

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“…Extremal properties of projective cubes have a vast literature, see e.g. [1,10,12,17]. The problem on forbidding d-dimensional projective cubes can be viewed as a generalization of sum-free sets in another direction, since a sum-free set is also a 2 -free set.…”

Section: Discussionmentioning

confidence: 99%

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

Jing

2020

Preprint

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Let M (2,1) (N ) denotes the infimum of the size of the largest sum-free subset of any set of N positive integers. An old conjecture in additive combinatorics asserts that there are a constant c = c(2, 1) and a function ωis determined by Eberhard, Green, and Manners, while the existence of ω(N ) is still widely open.In this paper, we study the analogue 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), and confirm the conjecture for infinitely many (k, ℓ).

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Section: Discussionmentioning

confidence: 99%