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I have the following problem

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I have asked the question here Writing a Permutation as a product of Disjoint Cycles and got the answer.Now how can i write this same permutation as a product of Transpositions.I know how to express it as a product of disjoint cycles and i know a transposition is a cycle with 2 elements.

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If you decompose into cycles first, all you need to do is express each cycle as a product of transpositions. There are various ways to do this, for example $$ (1\,2\,3\,4\,\ldots\,n) = (1\,n)\cdots(1\,4)(1\,3)(1\,2) $$ or $$ (1\,2\,3\,4\,\ldots\,n) = (1\,2)(2\,3)(3\,4)\cdots(n{-}1\;n) $$

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  • $\begingroup$ Hmm... I expressed the permutation as the product of disjoint cycles (1532)(4) then what should i do? $\endgroup$ – techno Oct 8 '15 at 11:27
  • $\begingroup$ @techno: As I wrote: "all you need to do is express each cycle as a product of permutations". $\endgroup$ – hmakholm left over Monica Oct 8 '15 at 11:27
  • $\begingroup$ @techno represent each cycle as a product of transpositions and put them together $\endgroup$ – Omnomnomnom Oct 8 '15 at 11:27
  • $\begingroup$ @Omnomnomnom well i dont know how to represent each cycle as a transposition.Noob here :) $\endgroup$ – techno Oct 8 '15 at 11:28
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    $\begingroup$ @techno: I suggest that you read my answer, immediately above this comment thread. It will tell you how to represent a cycle as a product of transpositions. $\endgroup$ – hmakholm left over Monica Oct 8 '15 at 11:29

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