Conjectures about Latin Squares
MOLS existence problem: determine exactly which orders n admit a complete set of n - 1 mutually orthogonal latin squares.
Mathematical statement
MOLS existence problem: determine exactly which orders n admit a complete set of n - 1
mutually orthogonal latin squares.
Equivalently, this asks for which orders affine planes of order n exist. Complete sets are known
for prime-power orders; the smallest currently unresolved order is 12.
Statement source: Papers 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
molsExistenceProblem
theorem molsExistenceProblem : answer(sorry) = {n : ℕ | HasCompleteMOLS 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