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arXiv · 2401.17507

On skew corner-free sets

Cosmin Pohoata·Dmitrii Zakharov
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Abstract

We construct skew corner-free sets in $[n]^2$ of size $n^{5/4}$, thereby disproving a conjecture of Kevin Pratt. We also show that any skew corner-free set in $\mathbb{F}_{q}^{n} \times \mathbb{F}_{q}^{n}$ must have size at most $q^{(2-c)n}$, for some positive constant $c$ which depends on $q$.

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Cosmin Pohoata, Dmitrii Zakharov. 2024-01-30. On skew corner-free sets. https://arxiv.org/abs/2401.17507

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