sorting a list and counting interchanges

[RickMuller]

>> 3. Of what practical use (or even esoteric academic interest) is the
>> parity of the number of interchanges?

>I presume the goal is academic, determining whether a >permutation is
a member of
>the alternating group of even permutations (A4, A5, ...).  For >some
problems,
>that is a useful invariant.  For instance, iirc, the parity
>determines whether a
>given 15 puzzle arrangement is solvable.

To tell whether a wave function corresponds to bosons or fermions.