SOLUTION: Determine the length of the cycle in a given permutation a. [1 2 3 4 5 6 7 8 4 1 5 6 7 8 3 2 ] b. [1 2 3 4 5 6 7 8 3 6 5 1 4 8 2 7 ]

Algebra ->  Permutations -> SOLUTION: Determine the length of the cycle in a given permutation a. [1 2 3 4 5 6 7 8 4 1 5 6 7 8 3 2 ] b. [1 2 3 4 5 6 7 8 3 6 5 1 4 8 2 7 ]       Log On


   

Question 1205094: Determine the length of the cycle in a given permutation
a. [1 2 3 4 5 6 7 8 4 1 5 6 7 8 3 2 ]
b. [1 2 3 4 5 6 7 8 3 6 5 1 4 8 2 7 ]


Answer by mccravyedwin(406) About Me  (Show Source):
You can put this solution on YOUR website!
Determine the length of the cycle in a given permutation
a.

First we determine its orbits:
1->4->6->8->2->1 so the first orbit is 
[1 4 6 8 2]

3->5->7->3 so the second orbit is
[3 5 7]

All the numbers 1-8 are used so that's all the orbits. There are 2 orbits.

%28matrix%285%2C1%2CThe%2Clength%2Cof%2Cthe%2Ccycle%29%29%22%22=%22%22%28matrix%287%2C1%2C%0D%0Athe%2C+number%2C+of%2C+elements%2C+in%2C+the%2C+permutation%29%29%22%22-%22%22

Therefore 

%28matrix%285%2C1%2CThe%2Clength%2Cof%2Cthe%2Ccycle%29%29%22%22=%22%228%22%22-%22%222%22%22=%22%226


b. [1 2 3 4 5 6 7 8] 
   [3 6 5 1 4 8 2 7]

Do this one the same way.

Edwin