sorting a list and counting interchanges

[RickMuller]

Well, it's a homework problem in the sense that I happen to be working
on it at my home, but, no, I'm not in school anymore. In Quantum
Mechanics we use determinants to enforce the Pauli principle, which
says that anytime two electrons are exchanged the wave function has to
change sign. In most Quantum Mechanical packages (for example,
PyQuante, http://pyquante.sf.net, which I wrote some years ago, is a
Python based quantum chemistry package) we don't actually have to
evaluate a determinant, we just evaluate the effect of the two-electron
operators on the permuted wave function. However, I'm working on some
quantum monte carlo codes where I'm trying to keep track of
configuration spin functions, which requires me to count every time I
flip orbitals.