Fetching the paper…
Reading the bibliography…
It has been recently proved (by Croot, Lev and Pach and the subsequent work by Ellenberg and Gijswijt) that for a group $G=G_0^n$, where $G_0\ne \{1,-1\}^m$ is a fixed finite Abelian group and $n$ is large, any subset $A$ without 3-progressions (triples $x,y,z$ of different elements with $xy=z^2$) contains at most $|G|^{1-c}$ elements, where $c>0$ is a constant depending only on $G_0$.
John E. Olson. A Combinatorial Problem on Finite Abelian Groups I, Journal of Number Theory, 1(1) (1969), 8–10
1969
Earlier work this paper cites.
Roy Meshulam. On the maximal rank in a subspace of matrices. The Quarterly Journal of Mathematics 36 (1985), no. 2, 225–229
1985
Earlier work this paper cites.
Noga Alon. Combinatorial Nullstellensatz, Combin. Probab. Comput. 8 (1999), 7–29
1999
Earlier work this paper cites.
Kevin O’Bryant. Sets of integers that do not contain long arithmetic progressions. Electronic Journal of Combinatorics 18 (1) (2011)
2011
Earlier work this paper cites.
2016
Cited alongside, same era.
Ernie Croot, Vsevolod Lev, and Peter Pach. Progression-free sets in ℤ 4 n \mathbb{Z}_{4}^{n} are exponentially small. Ann. of Math. 185 (2017), no. 1, 331–337
2017
Cited alongside, same era.
Jordan Ellenberg and Dion Gijswijt. On large subsets of 𝔽 𝕢 n \mathbb{F_{q}}^{n} with no three-term arithmetic progression. Ann. of Math. 185 (2017), no. 1, 339–343
2017
Cited alongside, same era.
Eric Naslund, Will Sawin. Upper bounds for sunflower-free sets. Forum Math. Sigma 5 (2017), e15, 10 pp
2017
Cited alongside, same era.
Ilya Bogdanov, the answer to Mathoverflow question. URL: http://mathoverflow.net/questions/239222/vector-with-many-non-zero-coordinates
Cited in the paper.
Jordan Ellenberg. Sumsets as unions of sumsets of subsets. Discrete Anal. (2017), Paper No. 14, 5 pp
2017
Closest in time.
Robert Kleinberg, Will Sawin, David Speyer. The growth of tri-colored sum-free sets, Discrete Anal. (2018), Paper No. 12, 10 pp
2018
Closest in time.
Luke Pebody. Proof of a Conjecture of Kleinberg-Sawin-Speyer, Discrete Anal. (2018), Paper No. 13, 7 pp
2018
Closest in time.
Sergey Norin. A distribution on triples with maximum entropy marginal. Forum Math. Sigma 7 (2019), e46
2019
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…