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