Optimal monotone families for the discrete isoperimetric inequality: Kahn Kalai Conjecture 7
Conjecture 7 from Kahn–Kalai 2006: the same statement as the original conjecture, but with the additional assumption that is the critical probability for , namely .
Mathematical statement
Conjecture 7 from Kahn–Kalai 2006: the same statement as the original conjecture, but with the additional assumption that is the critical probability for , namely .
Statement source: MathOverflow statement material
Statement terms: CC-BY-SA-4.0
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Statement artifacts, not proofs
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Pinned Lean formulation 1
mathoverflow_10799.variants.kahn_kalai_conjecture_7
theorem mathoverflow_10799.variants.kahn_kalai_conjecture_7 : answer(sorry) ↔ ∀ (n : ℕ) (_ : 2 ≤ n) (F : Finset (Finset (Fin n))) (_ : IsMonotoneIncreasing F) (s t : ℝ) (_ : 0 < s) (_ : s ≤ t) (_ : t < 1) (_ : μFamily t F = 1 / 2) (_ : t / s > 1000 * Real.log n), ∃ p, s ≤ p ∧ p ≤ t ∧ IsOptimal p F := 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