My Math Forum representation of permutation

 February 28th, 2013, 05:20 AM #1 Newbie   Joined: Feb 2013 Posts: 16 Thanks: 0 representation of permutation Let $\pi:\{1, \ldots, n\}\longrightarrow\{1, \ldots, n\}$. Fix first $m, m\leq n$ elements from $\{1, \ldots, n\}$ and consider permutations $\pi_1:\{1, \ldots, m\}\longrightarrow\{1, \ldots, m\}$ and $\pi_2:\{m+1, \ldots, n-m\}\longrightarrow\{m+1, \ldots, n-m\}$, where $\pi_1$ permute each element to itself. Question: How to introduce $\pi$ in terms of $\pi_2$? Work so far: Ofcourse, $\pi=\pi_1 \pi_2$, but now, how to introduce $\pi_1$ in terms of $\pi_2$.... Maybe one should use projections... I am stuck here. Thank you.
 February 28th, 2013, 07:47 AM #2 Senior Member   Joined: Feb 2013 Posts: 281 Thanks: 0 Re: representation of permutation When you write something like this p = p1p2, then supposedly all the three permutations act on the same set, unlike in your example.

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