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radou

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radou

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- #2

cristo

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Don't you just read from the right? So, (2 3)(1 2 3) is the permutation [tex]\left(\begin{array}{ccc}1&2&3\\3&2&1\end{array}\right)[/tex], since the right cycle sends 1 to 2, which in turn gets sent to 3 by the left cycle. The right cycle sends 2 to 3, which is then sent to 2 by the left cycle, and finally the right one sends 3 to 1, which remains unchanged by the left.

edit: That might be the way you say you do it. If so, I can't help, as that's the way I was taught!

edit: That might be the way you say you do it. If so, I can't help, as that's the way I was taught!

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radou

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I *finally* got it. Thanks cristo!Don't you just read from the right? So, (2 3)(1 2 3) is the permutation [tex]\left(\begin{array}{ccc}1&2&3\\3&2&1\end{array}\right)[/tex], since the right cycle sends 1 to 2, which in turn gets sent to 3 by the left cycle. The right cycle sends 2 to 3, which is then sent to 2 by the left cycle, and finally the right one sends 3 to 1, which remains unchanged by the left.

edit: That might be the way you say you do it. If so, I can't help, as that's the way I was taught!

- #4

cristo

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You're welcome!I *finally* got it. Thanks cristo!

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HallsofIvy

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Here's how I would do that problem:

(1 2 3) means "1 changes to 2, 2 changes to 3, and 3 changes to 1".

(2, 3) means "2 changes to 3 and 3 changes to 2".

Okay, putting them together, 1 changes to 2 and 2 changes to 3. so 1 changes to 3. 2 changes to 3 and 3 changes to 2, so 2 changes to 2. 3 changes to 1 and 1 does not change, 3 changes to 1.

1 changes to 3 and 3 changes to 1. 2 does not change. In cycle notation that is (1 3).

- #6

radou

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That's exactly how I got it. I was just trying to find a quick way to look at these, since they occur often in my textbook, at least in the current chapter.

Here's how I would do that problem:

(1 2 3) means "1 changes to 2, 2 changes to 3, and 3 changes to 1".

(2, 3) means "2 changes to 3 and 3 changes to 2".

Okay, putting them together, 1 changes to 2 and 2 changes to 3. so 1 changes to 3. 2 changes to 3 and 3 changes to 2, so 2 changes to 2. 3 changes to 1 and 1 does not change, 3 changes to 1.

1 changes to 3 and 3 changes to 1. 2 does not change. In cycle notation that is (1 3).

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matt grime

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