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

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- Mar 12th 2010, 11:42 AMcraigPermutations & 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 - Mar 12th 2010, 12:23 PMHaven
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 - Mar 12th 2010, 04:19 PMcraig