Corners in Quasirandom Groups via Sparse Mixing
Combinatorics
2025-04-14 v3 Computational Complexity
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).
Keywords
Cite
@article{arxiv.2411.02702,
title = {Corners in Quasirandom Groups via Sparse Mixing},
author = {Michael Jaber and Shachar Lovett and Anthony Ostuni},
journal= {arXiv preprint arXiv:2411.02702},
year = {2025}
}
Comments
This work has been subsumed by arXiv:2504.07006, which also fixes a technical issue present in the previous version