Is there a notation to denote the difference between these two products of cycles? It seems as though there are two conventions out there that should have a specific name for them. The subscripts for α: r uses the right to left convention and l uses the left to right convention. Not sure what else to call it.
α=(1,3,2)(4,2)
$α_r$=(1,3,2,4)
$α_l$=(1,3,4,2)