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refactor: More notes on Wick's thoerem

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jstoobysmith 2025-02-04 09:58:30 +00:00
parent 20df8ece6c
commit 034f6c8c91
6 changed files with 115 additions and 77 deletions
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5
HepLean/PerturbationTheory/WickContraction/IsFull.lean
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@ -48,6 +48,11 @@ def isFullInvolutionEquiv : {c : WickContraction n // IsFull c} ≃
left_inv c := by simp
right_inv f := by simp
remark card_in_general := "The cardinality of `WickContraction n` in general
follows OEIS:A000085. I.e.
1, 1, 2, 4, 10, 26, 76, 232, 764, 2620, 9496, 35696, 140152, 568504, 2390480,
10349536, 46206736, 211799312, 997313824,...."
/-- If `n` is even then the number of full contractions is `(n-1)!!`. -/
theorem card_of_isfull_even (he : Even n) :
Fintype.card {c : WickContraction n // IsFull c} = (n - 1)‼ := by