PermutationProduct¶

Composes permutations, applying them left to right. With permutation lists (image lists) the result is a permutation list; with Cycles objects the result is in Cycles form.

$ wo 'PermutationProduct[{2, 1, 3}, {1, 3, 2}]'
{3, 1, 2}

$ wo 'PermutationProduct[{2, 3, 1}, {2, 3, 1}, {2, 3, 1}]'
{1, 2, 3}

A shorter permutation list fixes points beyond its length:

$ wo 'PermutationProduct[{2, 1}, {2, 3, 1}]'
{3, 2, 1}

Cycles arguments compose to a Cycles object:

$ wo 'PermutationProduct[Cycles[{{1, 2}}], Cycles[{{2, 3}}]]'
Cycles[{{1, 3, 2}}]