Anonymous user
Talk:Sattolo cycle: Difference between revisions
m
order of elements
(I think *you* should re-read the wikipedia entry on cyclic permutations ;)) |
m (order of elements) |
||
Line 46:
::::: ''(...) given X = {1, 2, 3, 4}, the permutation (1, 3, 2, 4) that sends 1 to 3, 3 to 2, 2 to 4 and 4 to 1 (so S = X) is a 4-cycle, and the permutation (1, 3, 2) that sends 1 to 3, 3 to 2, 2 to 1 and 4 to 4 (so S = {1, 2, 3} and 4 is a fixed element) is a 3-cycle. '''On the other hand, the permutation that sends 1 to 3, 3 to 1, 2 to 4 and 4 to 2 is not a cyclic permutation because it separately permutes the pairs {1, 3} and {2, 4}.'''''
:::: You will notice that you can replace the set X = {1,
::::: '''''On the other hand, the permutation that sends A to B, B to A, C to D and D to C is not a cyclic permutation because it separately permutes the pairs {A, B} and {C, D}.'''''
| |||