sorting a list and counting interchanges

[Dan Bishop]

Paul Rubin wrote:
> John Machin <sjmachin at lexicon.net> writes:
...
> > 3. Of what practical use (or even esoteric academic interest) is
the
> > parity of the number of interchanges?
>
> It is of considerable interest in combinatorics.  The group of even
> permutations on N elements is called the alternating group A(N).
> It's an order-2 subgroup of the symmetric group S(N) which is the
> group of all the permutations on N elements.  The odd permutations
> are of course a coset of A(N).

It's also used in linear algebra, as part of the definition of the
determinant.