Re: Odd and even transpositions of permutations

In article <7uk6h4dkupkh9rh6pvde1n66b132n8pl5k@xxxxxxx>,
Ulysse from CH <ulysse@xxxxxxxxxxxxxxxxx> wrote:
On Wed, 5 Nov 2008 17:42:36 +0000 (UTC), magidin@xxxxxxxxxxxxxxxxx
(Arturo Magidin) wrote:

In article <aebb6a33-18c1-486a-a35c-992fb5bd9af5@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Billiam <tadej.slamic@xxxxxxxxx> wrote:
Hello,
I cannot see why there is (1/2)n! odd and (1/2)n! even transpositions
of permutations (if there is n! permutations).
"Transposition" means a permutation of order 2, [...]

not exactly, a product of two transpositions acting on 4 distinct
elements has order 2, but is not a transposition !
but every transposition has order 2
A transposition is a permutation that lets every element fixed
except two that it interchanges

Ah; I can never keep those straight. It doesn't matter: that still
makes the original question nonsense as written (there is no such
thing as a "transposition of permutation", let alone "odd
transposition of permutation" and "even transposition of
permtuation". He meant "even permutation" and "odd permutation".

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================

Arturo Magidin
magidin-at-member-ams-org

.

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