Source labels openChecked July 26, 2026

Conjectures about Latin Squares

Conjecture 6.9 in [Wa2011]: $\lim_{\substack{n \to \infty \\ n \text{ odd}}} \frac{1}{n} \log(z_n / n!) = -1$ It is not even known if this limit exists. Note that $z_n = 0$ for even $n$ (see z_even), so the limit must be restricted to odd $n$ ; here we...

Combinatorics AMS 5

Mathematical statement

Conjecture 6.9 in [Wa2011]:

\lim_{\substack{n \to \infty \\ n \text{ odd}}} \frac{1}{n} \log(z_n / n!) = -1

It is not even known if this limit exists. Note that $z_n = 0$ for even $n$ (see z_even), so the limit must be restricted to odd $n$ ; here we parametrise odd $n$ as $2k + 1$ .

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

growthRateZn

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem growthRateZn : answer(sorry) ↔    Filter.Tendsto (fun k => (1 : ℝ) / (2 * k + 1) *      Real.log (z (2 * k + 1) / (2 * k + 1).factorial)) Filter.atTop      (nhds (-1)) := 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