# cycle

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• February 25th 2009, 05:08 AM
wonjujin
cycle
show that if F is a cycle of odd length the F2 is a cycle
• February 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 $(12345)^2 = (13524)$ and $(1234567)^2 = (1357246)$ and in general $(1,2,...,2n+1)^2 = (1,3,...,2n+1,2,4,...,2n)$.