Permutation Operations

This calculator finds the inverse permutation, the number of inversions and the parity, the cycle decomposition and the order of a permutation.

Example. For the permutation 3 1 2 5 4 the inverse is 2 3 1 5 4, there are 3 inversions, the cycles are (1 3 2)(4 5) and the order is lcm(3, 2) = 6.

A permutation is even if the number of inversions is even. The order shows how many times to apply the permutation to return to the original arrangement.