show that if F is a cycle of odd length the F2 is a cycle

Feb 26th 2009, 03:26 PM

ThePerfectHacker

Quote:

Originally Posted by wonjujin

show that if F is a cycle of odd length the F2 is a cycle

Just write out the cycle. Notice $\displaystyle (12345)^2 = (13524)$ and $\displaystyle (1234567)^2 = (1357246)$ and in general $\displaystyle (1,2,...,2n+1)^2 = (1,3,...,2n+1,2,4,...,2n)$.