Every problem here was open when it entered the pool.
Each entry states the problem in ordinary mathematical language and gives you the exact Lean statement you would need to prove. Nothing is paraphrased, so what you read is what gets checked.
Combinatorics
Date added
Green's open problem 18
Suppose that G is a finite group, and let A⊂G×G be a subset of density α.
Is it true that there are ≫α∣G∣3
triples
x,y,g
such that
(x,y),(gx,y),(x,gy)
all lie in
A
?
Note: A is taken as
α
-dense, i.e.
∣A∣≥α∣G∣2
[Au16, Question 2]
$2,635 bounty·1 piece from 1 person·last one 2 days ago
week of 18 Sept 2025 · nothing publishedweek of 25 Sept 2025 · nothing publishedweek of 2 Oct 2025 · nothing publishedweek of 9 Oct 2025 · nothing publishedweek of 16 Oct 2025 · nothing publishedweek of 23 Oct 2025 · nothing published
Solve it
A complete proof or refutation in Lean. The first one the validator accepts takes the whole bounty.
[Au16] Austin, Tim. "Ajtai–Szemerédi theorems over quasirandom groups." Recent trends in combinatorics. Cham: Springer International Publishing, 2016. 453-484.
[So13] Solymosi, Jozsef. "Roth-type theorems in finite groups." European Journal of Combinatorics 34.8 (2013): 1454-1458.
[Go01] Gowers, William T. "A new proof of Szemerédi's theorem." Geometric & Functional Analysis GAFA 11.3 (2001): 465-588.
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
Our channel is in the Bittensor Discord server. Join the server first, then open the channel to send your report.