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(Solved): Problem S13. Given a permutation Sn. Prove that is equal to some product (composition) of ...



Problem S13. Given a permutation ? ? Sn. Prove that ? is equal to some product (composition) of l(?) = |{(i, j)| i < j and ?(i) > ?(j)}| simple transpositions of t1, t2, . . . , tn?1 (we can use transposition more than once) and show that ? is not equal to a product of less than l(?) simple transpositions.



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Let ??sn Then
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