# conjugacyClass(List) -- the conjugacy class of a permutation

## Synopsis

• Function: conjugacyClass
• Usage:
conjugacyClass perm
• Inputs:
• perm, a list, a permutation of the list of numbers from 0 to n-1
• Outputs:
• an instance of the type Partition, a partition that represents the conjugacy class of the permutation

## Description

The method first calculates the cycle decomposition of the permutation Then the conjugacy class is the partition given by the lengths of the cycles in the decomposition

 i1 : cycleDecomposition {0,1,2,3,4} o1 = {{0}, {1}, {2}, {3}, {4}} o1 : List i2 : conjugacyClass {0,1,2,3,4} o2 = Partition{1, 1, 1, 1, 1} o2 : Partition i3 : cycleDecomposition {1,3,2,0,4} o3 = {{0, 1, 3}, {2}, {4}} o3 : List i4 : conjugacyClass {0,1,2,3,4} o4 = Partition{1, 1, 1, 1, 1} o4 : Partition