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Paper:

TR24-170 | 5th November 2024 03:03

Corners in Quasirandom Groups via Sparse Mixing

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TR24-170
Authors: Michael Jaber, Shachar Lovett, Anthony Ostuni
Publication: 5th November 2024 04:53
Downloads: 256
Keywords: 


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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