Place-permutation action

Summary

In mathematics, there are two natural interpretations of the place-permutation action of symmetric groups, in which the group elements act on positions or places. Each may be regarded as either a left or a right action, depending on the order in which one chooses to compose permutations. There are just two interpretations of the meaning of "acting by a permutation $\sigma$" but these lead to four variations, depending whether maps are written on the left or right of their arguments. The presence of so many variations often leads to confusion. When regarding the group algebra of a symmetric group as a diagram algebra it is natural to write maps on the right so as to compute compositions of diagrams from left to right.