| सारांश: | <p>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.</p>
<p>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).</p>
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