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Deveno
Deveno is offline
#21
Nov23-11, 04:49 PM
Sci Advisor
P: 906
this is how i count n-cycles in Sn (this works for any n, but i will use n = 4):

since any 4-cycle in S4 involves 1, we may as well start with it:

(1.....

i have 3 choices for my next element (the image of 1):

(1 2.....
(1 3.....
(1 4.....

after i make my next choice, i'll have them all:

(1 2 3 4)
(1 2 4 3)
(1 3 2 4)
(1 2 4 2)
(1 4 3 2)
(1 4 2 3)

that makes 6.

in general, in Sn, we'll get (n-1)(n-2)....(2) = (n-1)! possible distinct n-cycles.