intersecting_permutation_families

⚠️ 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.

t-Intersecting permutation families: A family of permutations where any two agree in at least t positions has size at most (n-t)!. Proved for t=1; open for general t.

Why this node was retired

The posted statement is

import Mathlib

theorem intersecting_permutation_families (n t : ℕ) (hn : 1 ≤ n) (ht : 1 ≤ t) (htln : t ≤ n)
    (F : Finset (Equiv.Perm (Fin n)))
    (hint : ∀ sigma ∈ F, ∀ tau ∈ F, t ≤
      ((Finset.univ (α := Fin n)).filter (fun i => sigma i = tau i)).card) :
    F.card ≤ (n - t).factorial := by
  sorry

The bound is claimed for every n≥t, omitting a sufficient size threshold relative to t.

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

Proposed corrected statement

For each fixed t require n≥N(t) as in the intended large-n theorem; specify the appropriate established threshold rather than only t≤n.

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.