  QCD at fixed baryon number can be formulated in terms of transfer matrices
explicitly defined in the canonical sectors. In the heavy-dense limit, the
fermionic contributions to the canonical partition functions in terms of
Polyakov loops and quark occupation numbers turn out to be completely
factorized in space. At low temperatures and infinitely strong coupling the
sign problem is reduced by orders of magnitude for any baryon number as
compared to the corresponding grand-canonical ensemble. In the canonical
formulation it is straighforward to integrate out the Polyakov loops in the
fermionic weights yielding the partition function as a sum of only baryon
occupation numbers in which the sign problem is absent. Using an effective form
of the gauge action valid for small values of the gauge coupling, the same can
be achieved away from the strong coupling limit in terms of quark occupation
numbers and fluxes which couple the quarks with each other. The emerging
clusters suggest the construction of algorithms which circumvent the sign
problem in the heavy-dense limit including the full gauge action for any value
of the gauge coupling.
