steins_conjecture_latin_transversal

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

Stein's conjecture (1975): Every n×n Latin square has a partial transversal of length n-1 (and most have a full transversal). Ryser (1967) conjectured all odd-order Latin squares have full transversals. Hatami-Shor (2008) proved length n - O(log²n). The conjecture of a full transversal of length n remains open.

Why this node was retired

The posted statement is

import Mathlib

theorem steins_conjecture_latin_transversal (n : ℕ) (hn : 1 ≤ n)
    (L : Fin n → Fin n → Fin n)
    (hrow : ∀ i : Fin n, Function.Injective (L i))
    (hcol : ∀ j : Fin n, Function.Injective (fun i => L i j)) :
    ∃ (tau : Fin n → Fin n), Function.Bijective tau ∧
      Function.Injective (fun i => L i (tau i)) := by
  sorry

A partial transversal of length n−1 is replaced by a full transversal for every order.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

Ask for n−1 cells with distinct row, column, and symbol; or restrict to odd n if the intended problem is Ryser’s full-transversal conjecture.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.