# Math Help - Cycle notation

1. ## Cycle notation

Hi guys,

I need help understanding cycle notation. Can you work me through this example please?

Kind regards,

Banana

2. Originally Posted by Banana1
Hi guys,

I need help understanding cycle notation. Can you work me through this example please?

Kind regards,

Banana

Begin by "going" with the numbers beginning with 1: 1 goes to 2, 2 goes to 3, 3 goes to 1: we closed a first cycle (123); 4 goes to 4 and we don't write it, and then 5 goes to 6 and 6 goes to 5 ==> another cyce (56), so finally $\sigma=(123)(56)$ , and you have to read this as "1 -> 2 -> 3->1, 5->6->5.
Note that we didn't write the cycle (4): 4 goes to 4. This can be confusing sometimes if we don't know what n in $S_n$ are we working with, but in most cases we do so if we don't see a one-number cycle it means the permutation maps it to itself.
Now you try with $\pi$ (you've got to get one single 4-cycle)

Finally a warning word: when you multiply cycles, most authors choose to do it from right to left, as in functions composition.

Tonio

3. ## Cycle notation

Thanks mate,

Can anyone help me with the inverse, my memory is not great.

Cheers,

Banana

4. Originally Posted by Banana1
Thanks mate,

Can anyone help me with the inverse, my memory is not great.

Cheers,

Banana

Take the permutation and put it upside down: put the numbers of the second row in the first one and in the 2nd row put the first one...according to the order they were.
Thus, if 1 --> 3, then in the inverse 3 -->1 and etc.

Tonio