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We construct an $S_3$-symmetric probability distribution on $\{(a,b,c) \in \mathbb{Z}_{\geq 0}^3 \: : \: a+b+c =n \}$ such that its marginal achieves the maximum entropy among all probability distributions on $\{0,1,\ldots,n\}$ with mean $n/3$.
On cap sets and the group-theoretic approach to matrix multiplication
Jonah Blasiak, Thomas Church, Henry Cohn, Joshua A. Grochow, Eric Naslund, William F. Sawin, and Chris Umans · 2017
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Progression-free sets in ℤ 4 n \mathbb{Z}^{n}_{4} are exponentially small
Ernie Croot, Vsevolod F. Lev, and Péter Pál Pach · 2017
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On large subsets of 𝔽 q n \mathbb{F}^{n}_{q} with no three-term arithmetic progression
Jordan S. Ellenberg and Dion Gijswijt · 2017
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A tight bound for Green’s arithmetic triangle removal lemma in vector spaces
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The growth rate of tri-colored sum-free sets
Robert Kleinberg, Will Sawin, and David E. Speyer · 2018
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Proof of a conjecture of Kleinberg-Sawin-Speyer
Luke Pebody · 2018
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