Definition 11: Let Sn, and let oESn. We say that o is a d-cycle if there are integers i1; 2;…; id such that o(i1)=i2,σ(2)=i3, andσ(d=i1andσ fixes every other integer, …la-1lala+1 O        = + − + d d n d d d n i i i i i i i i i i i i     2 3 1 1 1 2 1 1   Definition 11: Let |S|=n, and let Sn .We say that  is a d-cycle if there are integers i1 ; i2 ; … ; id such that (i1 ) =i2 , (i2 ) = i3 , … , and (id ) =i1 and  fixes every other integer, i.e