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arXiv · 2411.02702

Corners in Quasirandom Groups via Sparse Mixing

Michael Jaber·Shachar Lovett·Anthony Ostuni
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Abstract

We improve the best known upper bounds on the density of corner-free sets over quasirandom groups from inverse poly-logarithmic to quasi-polynomial. We make similarly substantial improvements to the best known lower bounds on the communication complexity of a large class of permutation functions in the 3-player Number-on-Forehead model. Underpinning both results is a general combinatorial theorem that extends the recent work of Kelley, Lovett, and Meka (STOC'24), itself a development of ideas from the breakthrough result of Kelley and Meka on three-term arithmetic progressions (FOCS'23).

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Michael Jaber, Shachar Lovett, Anthony Ostuni. 2024-11-05. Corners in Quasirandom Groups via Sparse Mixing. https://arxiv.org/abs/2411.02702

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