Source labels openChecked July 26, 2026

Green's Open Problem 51

Suppose that $A \subset \mathbb{F}_2^n$ is a set of density $\alpha$ . What is the largest size of coset guaranteed to be contained in $2A$ ?

Combinatorics AMS 5 AMS 11

Mathematical statement

Suppose that $A \subset \mathbb{F}_2^n$ is a set of density $\alpha$ . What is the largest size of coset guaranteed to be contained in $2A$ ?

We phrase this by asking for the exact function $F(\alpha, n)$ giving the maximum dimension of a guaranteed coset.

Statement source: Green's Open Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

green_51

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_51 : answer(sorry) = guaranteedMaxCosetDim := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization Green's Open Problemsbackground