  The delta set of a numerical semigroup $S$, denoted $\Delta(S)$, is a
factorization invariant that measures the complexity of the sets of lengths of
elements in $S$. We study the following problem: Which finite sets occur as the
delta set of a numerical semigroup $S$? It is known that $\min \Delta(S) = \gcd
\Delta(S)$ is a necessary condition. For any two-element set $\{d,td\}$ we
produce a semigroup $S$ with this delta set. We then show that for $t\ge 2$,
the set $\{d,td\}$ occurs as the delta set of some numerical semigroup of
embedding dimension three if and only if $t=2$.

Commutative Algebra;Combinatorics