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Source labels openChecked July 26, 2026

Green's Open ProblemsCombinatorics

Ben Green's Open Problem 72

The no-k-in-line problem: For N≥kN \geq k and k>2k > 2, the AllowedSetSize is (k−1)N(k - 1) N, i. e. on an N×NN \times N subset, there is a set of (k−1)N(k - 1) N points for which no kk lie on a line (and not such a set of bigger size).

CombinatoricsAMS 5AMS 52

Mathematical statement

The no-k-in-line problem: For N≥kN \geq k and k>2k > 2, the AllowedSetSize is (k−1)N(k - 1) N, i. e. on an N×NN \times N subset, there is a set of (k−1)N(k - 1) N points for which no kk lie on a line (and not such a set of bigger size).

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

NoKInLine

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem NoKInLine {k : ℕ} {N : ℕ} (hk : 2 < k) (h : k ≤ N) : NoKInLineFor k N := 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 sourceformalizationBen Green's Open Problem 72backgroundWikipediabackground