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- Apr 14, 2013

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Hey!!

We have the following permutations in $\text{Sym}(14)$ :

- $\pi_1=(1 \ 2\ 4 \ 9)\circ(1 \ 3)\circ (6 \ 8\ 12)$

- $\pi_2=(2 \ 4\ 5 \ 8\ 7)\circ (1 \ 12 \ 6)\circ \ (13 \ 14)$

- $\pi_3=(1 \ 4 \ 5\ 8 \ 11)\circ (2 \ 4\ 6 \ 5 \ 1)$

1. Determine the cycle decomposition of $\pi_1, \pi_2, \pi_3$.

2. Determine $\pi_1^{-1}, \pi_2^{-1}, \pi_3^{-1}$.

3. Determine $\pi_4=\pi_1\circ \pi_2$, $\pi_5=\pi_2\circ\pi_3$, $\pi_6=\pi_2\circ\pi_1$.

4. Determine the signum of $\pi_1, \pi_2, \pi_3, \pi_4, \pi_5, \pi_6$.

1. We consider the composition fromright to left, or not? Thenfrom the last we consider the element $6$ that goes $8$ and since there is no other $8$ previously we have that $6\rightarrow 8$.

Is this the idea to get the cycles?

2. We get the inverse permutation by the cycle decompsition, right?

We have the following permutations in $\text{Sym}(14)$ :

- $\pi_1=(1 \ 2\ 4 \ 9)\circ(1 \ 3)\circ (6 \ 8\ 12)$

- $\pi_2=(2 \ 4\ 5 \ 8\ 7)\circ (1 \ 12 \ 6)\circ \ (13 \ 14)$

- $\pi_3=(1 \ 4 \ 5\ 8 \ 11)\circ (2 \ 4\ 6 \ 5 \ 1)$

1. Determine the cycle decomposition of $\pi_1, \pi_2, \pi_3$.

2. Determine $\pi_1^{-1}, \pi_2^{-1}, \pi_3^{-1}$.

3. Determine $\pi_4=\pi_1\circ \pi_2$, $\pi_5=\pi_2\circ\pi_3$, $\pi_6=\pi_2\circ\pi_1$.

4. Determine the signum of $\pi_1, \pi_2, \pi_3, \pi_4, \pi_5, \pi_6$.

1. We consider the composition fromright to left, or not? Thenfrom the last we consider the element $6$ that goes $8$ and since there is no other $8$ previously we have that $6\rightarrow 8$.

Is this the idea to get the cycles?

2. We get the inverse permutation by the cycle decompsition, right?

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