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e5a97c6 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 | import Mathlib
namespace OAI
/-!
# A robust four-row permanent inequality
`Fin 4` labels four sites. A law is represented by real probability masses;
`IsProbability` asserts nonnegativity and total mass one. All row norms use
the uniform counting normalization.
-/
noncomputable section
namespace FourRow
open scoped BigOperators
abbrev Site := Fin 4
abbrev Perm := Equiv.Perm Site
abbrev Law := Perm → ℝ
abbrev Functions := Site → Site → ℝ
def IsProbability (ν : Law) : Prop :=
(∀ π, 0 ≤ ν π) ∧ ∑ π, ν π = 1
def UniformMarginals (ν : Law) : Prop :=
∀ i j : Site, ∑ π, (if π i = j then ν π else 0) = 1 / 4
def totalVariation (ν : Law) : ℝ :=
(∑ π, |ν π - 1 / 24|) / 2
def lpNorm (p : ℝ) (f : Site → ℝ) : ℝ :=
((∑ j, (f j) ^ p) / 4) ^ (1 / p)
def permanentExpectation (ν : Law) (f : Functions) : ℝ :=
∑ π, ν π * ∏ i, f i (π i)
end FourRow
end
end OAI
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