Corners in Quasirandom Groups via Sparse Mixing
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915236394565632 |
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| author | Jaber, Michael Lovett, Shachar Ostuni, Anthony |
| author_facet | Jaber, Michael Lovett, Shachar Ostuni, Anthony |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02702 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Corners in Quasirandom Groups via Sparse Mixing Jaber, Michael Lovett, Shachar Ostuni, Anthony Combinatorics Computational Complexity 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). |
| title | Corners in Quasirandom Groups via Sparse Mixing |
| topic | Combinatorics Computational Complexity |
| url | https://arxiv.org/abs/2411.02702 |