7
$\begingroup$

How we can show every permutation is either even or odd,but not both......I can't arrive at a proof for this ..... Can anybody give me the proof...

Thanks in advance...

  • 0
    There are three well explained answers to this question on http://en.wikipedia.org/wiki/Parity_of_a_permutation2010-09-16
  • 1
    Unless I'm having a particularly daft day... I question the validity of the first two proofs on wikipedia: they don't seem to eliminate the possibility that every permutation is both even and odd.2010-09-16
  • 1
    The identity permuation is even.2010-09-16
  • 3
    Depends on your definition of parity of the permutation. If you simply define it as the parity of number of inversion pairs, this is a no-brainer.2010-09-16
  • 0
    See my answer here: http://math.stackexchange.com/questions/46403/alternative-proof-that-the-parity-of-permutation-is-well-defined/46476#464762012-02-18

4 Answers 4