  Every set of natural numbers determines a generating function convergent for
$q \in (-1,1)$ whose behavior as $q \rightarrow 1^-$ determines a germ. These
germs admit a natural partial ordering that can be used to compare sets of
natural numbers in a manner that generalizes both cardinality of finite sets
and density of infinite sets. For any finite set $D$ of positive integers, call
a set $S$ "$D$-avoiding" if no two elements of $S$ differ by an element of $D$.
We study the problem of determining, for fixed $D$, all $D$-avoiding sets that
are maximal in the germ order. In many cases, we can show that there is exactly
one such set. We apply this to the study of one-dimensional packing problems.
