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On skew corner-free sets

Cosmin Pohoata, Dmitrii Zakharov

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 $q$.

On skew corner-free sets

Abstract

We construct skew corner-free sets in of size , thereby disproving a conjecture of Kevin Pratt. We also show that any skew corner-free set in must have size at most , for some positive constant which depends on .
Paper Structure (3 sections, 3 theorems, 15 equations)

This paper contains 3 sections, 3 theorems, 15 equations.

Table of Contents

  1. Introduction
  2. Proof of Theorem 1.1
  3. Proof of Theorem 1.2

Key Result

Theorem 1.1

There exists a skew corner-free set $S \subset [n]^2$ of size $\Omega(n^{5/4})$.

Theorems & Definitions (3)

  • Theorem 1.1
  • Theorem 1.2
  • Lemma 3.1