In , let
I found the cycle decomposition of to be , the question then asks me what is the cycle length of .
This is probably a stupid question but is it cycle length 4? I think I missed that small part of the lecture...
Thanks in advance
In , let
I found the cycle decomposition of to be , the question then asks me what is the cycle length of .
This is probably a stupid question but is it cycle length 4? I think I missed that small part of the lecture...
Thanks in advance
In Cycle notation, 1-cycles are often omitted, so you can right
So, we are left with a cycle of length 3 (since it permutes 3 numbers)
Now if we want to determine if this is an even or odd permutation, we must decompose into transpositions (2-cycles)
so,
Since there are 2 transpositions, is an even permutation