  A sequence of non-negative integers is exactly realizable as the fixed point
counts sequence of a dynamical system if and only if it gives rise to a
sequence of non-negative orbit counts. This provides a simple realizability
criterion based on the transformation between fixed point and orbit counts.
Here, we extend the concept of exact realizability to realizability of integer
sequences as differences of the two fixed point counts sequences originating
from a dynamical system and a topological factor. A criterion analogous to the
one for exact realizability is given and the structure of the resulting set of
integer sequences is outlined.
