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# foataBijection -- computes the image of a permutation under the Foata bijection

- Usage:
    `foataBijection w`
- Inputs:
  - w, a permutation,
- Outputs:
  - a permutation,

## Description

Foata's fundamental bijection is a bijection between a permutation's standard cycle decomposition and another permutation read the same (in one-line notation) as the decomposition with its parentheses removed. For example, if $p = (3 \, 2 \, 1)(5 \, 4)$ (written in cycle notation), then its corresponding permutation (written in one-line notation) is $\hat{p} = (3 \, 2 \, 1 \, 5 \, 4)$.

    i1 : p = permutation {3,1,2,5,4}

    o1 = Permutation{3, 1, 2, 5, 4}

    o1 : Permutation

    i2 : foataBijection p

    o2 = Permutation{3, 2, 1, 5, 4}

    o2 : Permutation

## Ways to use foataBijection:

- `foataBijection(Permutation)`

## For the programmer

The object foataBijection is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Permutations/Documentation/mainDocs.m2:329:0.