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I Is there a proof for this? n!/2

  1. Oct 13, 2016 #1
    is there a proof that the number of even/odd permutation matrices of any nxn, where n is greater than 3, is n!/2? basically, i want to understand the derivation of n!/2. thank you!
     
  2. jcsd
  3. Oct 13, 2016 #2

    mfb

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    It is easy to show that (a) there are in total n! permutation matrices and (b) there is a bijective function between odd and even permutations (e.g. swap two images). Combine both and you get n!/2 odd and n!/2 even permutations.
     
  4. Oct 13, 2016 #3
    how can i show the bijectiveness? sorry if my question is stupid
     
  5. Oct 13, 2016 #4

    mfb

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    By constructing it. For each even permutation, find exactly one unique odd permutation, or vice versa. I gave an example how to do that.
     
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