  This paper examines the relationship between the escape rate and the minimal
period of the hole. We consider a subshift of finite type on $q$ symbols with a
union of $t$ cylinders based at words of identical length $p$ as the hole. The
escape rate into the hole relates to the asymptotic behavior of the number of
words of fixed length that do not contain the fixed set of (forbidden) words at
which the cylinders are based. We explore the relationship between the escape
rate and $r(z)$, a rational function of the correlations between the forbidden
words. In particular, we prove that there exists a constant $D(t,p)$ such that
if $q>D(t,p)$, then the escape rate is faster for the hole with larger value of
$r(z)$ evaluated at $D(t,p)$. Further, we consider two holes each of which is a
union of cylinders based at words of equal length, having zero
cross-correlation, and prove that the larger is the minimal period of the
collection, the faster is the escape rate. However, when the cross-correlations
are non-zero, we give examples to prove that this result fails to hold. Our
results are more general than the existing ones known for maps conjugate to a
full shift with a single cylinder as the hole. The existing results arise as a
special case of our results.
