# The largest (k, l)-sum free subsets.

@inproceedings{Jing2020TheL, title={The largest (k, l)-sum free subsets.}, author={Yifan Jing}, year={2020} }

Let $\mathscr{M}_{(2,1)}(N)$ 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 $\omega(N)\to\infty$ as $N\to\infty$, such that $cN+\omega(N) 0$. The constant $c(2,1)$ is determined by Eberhard, Green, and Manners, while the existence of $\omega(N)$ is still widely open.
In this paper, we study the analogue conjecture on $(k,\ell)$-sum free… CONTINUE READING

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