  We analytically derive a decomposition of the lattice fermion determinant for
Wilson's Dirac operator with chemical potential into winding sectors, i.e.,
factors with a fixed number of quarks. Dividing the lattice into four domains,
the determinant is factorized into terms which can be classified with respect
to the winding number of the closed loops they consist of. The individual
factors are expressed in terms of subdeterminants and propagators on the
domains of the lattice. We numerically analyze properties of the factorization
formula and discuss two applications for the determination of canonical
partition functions with a fixed quark number: A speedup for the Fourier
transformation technique through a dimensional reduction, and a power series
expansion.
