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We prove new lower bounds on the maximum size of subsets $A\subseteq \{1,\dots,N\}$ or $A\subseteq \mathbb{F}_p^n$ not containing three-term arithmetic progressions.
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2004
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2004
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J. Blasiak, T. Church, H. Cohn, J. A. Grochow, E. Naslund, W. F. Sawin, and C. Umans, On cap sets and the group-theoretic approach to matrix multiplication
2017
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E. Croot, V. F. Lev, and P. P. Pach, Progression-free sets in ℤ 4 n \mathbb{Z}_{4}^{n} are exponentially small
2017
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J. S. Ellenberg and D. Gijswijt, On large subsets of 𝔽 q n \mathbb{F}_{q}^{n} with no three-term arithmetic progression
2017
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J. Fox and H. T. Pham, Popular progression differences in vector spaces II
2019
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C. Elsholtz and P. P. Pach, Caps and progression-free sets in ℤ m n \mathbb{Z}_{m}^{n}
2020
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B. Green and J. Wolf, A note on Elkin’s improvement of Behrend’s construction
2010
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M. Elkin, An improved construction of progression-free sets
2011
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T. Sanders, On Roth’s theorem on progressions
2011
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H. Lipmaa, Progression-free sets and sublinear pairing-based non-interactive zero-knowledge arguments
2012
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T. Sanders, On certain other sets of integers
2012
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N. Alon, A. Shpilka, and C. Umans, On sunflowers and matrix multiplication
2013
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2020
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2023
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C. Elsholtz, G. F. Lipnik, and M. Siebenhofer, New constructions of large caps
2023
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2023
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Z. Kelley and R. Meka, Strong bounds for 3-Progressions
2023
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S. Peluse, Finite field models in arithmetic combinatorics – twenty years on
2023
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F. Tyrrell, New lower bounds for cap sets
2023
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E. Naslund, Lower bounds for the Shannon Capacity of Hypergraphs
2024
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