<s>[INST] Permutation in discrete math Is the permutation 
$$\begin{pmatrix} 1& 2 &3 &4 &5 &6&7 \\ 7 & 4 & 2 & 1 & 3 & 6 & 5 \end{pmatrix}$$
even or odd?
The product of disjoint cycles is $$\begin{pmatrix}1& 7&5&3&2&4\end{pmatrix}\begin{pmatrix}6\end{pmatrix}$$
and the transposition are $$\begin{pmatrix}1 & 7 \end{pmatrix}\begin{pmatrix}1 & 5 \end{pmatrix}\begin{pmatrix}1 & 3\end{pmatrix}\begin{pmatrix}1 & 2 \end{pmatrix}\begin{pmatrix}1 & 4 \end{pmatrix}\begin{pmatrix}6 \end{pmatrix}$$ is it correct?
and the answer is even??
I feel confused about this..
 [/INST] This is as you said $$(1,7,5,3,2,4),$$
and then it is equal to 
$$(1,7)(7,5)(5,3)(3,2)(2,4),$$
and hence it is odd.
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