OAI/Combinatorics/ContingencyTables/Dense/DenseBooleanWalk.lean

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4 declarations, 0 contain sorry, 0 declared as axioms

The dense bin draw as one bounded unbiased Boolean word

  1. def OAI.ContingencyTables.GridBoundary.gridWordEquiv line 16
  2. def OAI.ContingencyTables.GridBoundary.denseBooleanWalk line 22
  3. def OAI.ContingencyTables.GridBoundary.denseBooleanWalkLaw line 27
  4. theorem OAI.ContingencyTables.GridBoundary.denseBooleanWalkLaw_eq line 33

    Source documentation

    Exactly n*(q_bin+8d^5) unbiased bits give the rational n-step law.

    theorem denseBooleanWalkLaw_eq (R : Option I → ℕ) (P : Option J → ℕ)
    (d : ℕ) (hd : 14 ≤ d) (hR : ∀ i, d ^ 12 ≤ R i) (hP : ∀ j, d ^ 12 ≤ P j)
    (hRmax : ∀ i, R (some i) ≤ R none) (hPmax : ∀ j, P (some j) ≤ P none)
    (hdimR : Fintype.card (Option I) ≤ d) (hdimP : Fintype.card (Option J) ≤ d)
    (hfree : Fintype.card (I × J) ≤ d) (htotal : ∑ i, R i = ∑ j, P j)
    (e : I × J ≃ Fin q) (a : Grid (I := Fin q) (4 * d ^ 8)) (n : ℕ) :
…

    Mentions: OAI.ContingencyTables.GridBoundary.Grid