feat: Add contraction involution file
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HepLean/PerturbationTheory/Contractions/Involutions.lean
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HepLean/PerturbationTheory/Contractions/Involutions.lean
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/-
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Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Joseph Tooby-Smith
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-/
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import HepLean.PerturbationTheory.Contractions.Basic
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import HepLean.Meta.Informal.Basic
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/-!
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# Involutions
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There is an isomorphism between the type of contractions of a list `l` and
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the type of involutions from `Fin l.length` to `Fin l.length`.
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Likewise, there is an isomorphism from the type of full contractions of a list `l`
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and the type of fixed-point free involutions from `Fin l.length` to `Fin l.length`.
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Given this, the number of full contractions of a list `l` is
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is given by the OEIS sequence A000085.
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-/
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namespace Wick
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open HepLean.List
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open FieldStatistic
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variable {𝓕 : Type}
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namespace Contractions
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variable {l : List 𝓕}
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informal_definition equivInvolution where
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math :≈ "There is an isomorphism between the type of contractions of a list `l` and
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the type of involutions from `Fin l.length` to `Fin l.length."
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informal_definition equivFullInvolution where
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math :≈ "There is an isomorphism from the type of full contractions of a list `l`
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and the type of fixed-point free involutions from `Fin l.length` to `Fin l.length."
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end Contractions
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end Wick
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@ -9,7 +9,6 @@ import HepLean.PerturbationTheory.Wick.SuperCommute
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# Operator map
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-/
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namespace Wick
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noncomputable section
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