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Tagged with sumsets arithmetic-progression
2
questions
5
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2
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Progressions in sumset or complement
Fix $\epsilon>0$.
For all large $N$, does there exist $A\subset [N]:=\{1,\dots,N\}$ such that both $A+A$ and $A^c:=[N]\setminus A$ lack arithmetic progressions of length $N^\epsilon$?
I am aware ...
- 2,874
3
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0
answers
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What's known about $X$ when $|X(n) + X(n)| < kn$, $n \in \mathbb{N}$, absolute constant $k$?
Let $X$ be an infinite sequence of integers$$x_1 < x_2 < x_3 < \ldots,$$and let $X(n)$ be the set$$\{x_1, x_2, \ldots, x_n\}.$$
Question. What is known about $X$ when we have$$|X(n) + X(n)| &...
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