Thread: Permutations & Cycles

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

Originally Posted by Haven

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

Of course, 1 cycles just send the number to itself. Thanks for the reply, appreciate it.