HW due Monday (short)

1. Let pi be a permutation of {1..n}. When written out in cycle notation (including each i s.t. pi(i)=i as a cycle of length 1), let k be the number of cycles.

Let (i j) be the permutation that switches i and j, and leaves the other elements alone. (So this permutation has n-1 cycles, according to the definition above.)

Show that the product pi * (i j) has either k-1 or k+1 cycles, and explain when it's k-1 and when it's k+1.

5.3 #34,35,38