# cycleDecomposition(List) -- the cycle decomposition of a permutation

## Synopsis

• Function: cycleDecomposition
• Usage:
cycleDecomposition perm
• Inputs:
• perm, a list, a permutation of the list of numbers from 0 to n-1
• Outputs:
• a list, a doubly nested list with cycles of the permutation

## Description

Every permutation has a decomposition as the concatenation of disjoint cycles. This decomposition is used to calculate the conjugacy class of the permutation.

 i1 : cycleDecomposition {0,1,2,3,4} o1 = {{0}, {1}, {2}, {3}, {4}} o1 : List i2 : cycleDecomposition {1,3,2,0,4} o2 = {{0, 1, 3}, {2}, {4}} o2 : List