  We have explained in detail why the canonical partition function of
Interacting Self Avoiding Walk (ISAW), is exactly equivalent to the
configurational average of the weights associated with growth walks, such as
the Interacting Growth Walk (IGW), if the average is taken over the entire
genealogical tree of the walk. In this context, we have shown that it is not
always possible to factor the the density of states out of the canonical
partition function if the local growth rule is temperature-dependent. We have
presented Monte Carlo results for IGWs on a diamond lattice in order to
demonstrate that the actual set of IGW configurations available for study is
temperature-dependent even though the weighted averages lead to the expected
thermodynamic behavior of Interacting Self Avoiding Walk (ISAW).
