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 Permutations/Documentation/mainDocs.m2:329:0.