An affine semigroup is a finitely generated subsemigroup of
,
and a numerical semigroup is an affine semigroup with
.
A growing body of recent work examines shifted families of numerical
semigroups, that is, families of numerical semigroups of the form
for
fixed
,
with one semigroup for each value of the shift parameter
.
It has been shown that within any shifted family of numerical semigroups, the
size of any minimal presentation is bounded (in fact, this size is eventually periodic in
). We
consider shifted families of affine semigroups, and demonstrate that some, but not all,
shifted families of 4-generated affine semigroups have arbitrarily large minimal presentations.
