  Let $ S_g $ be a closed surface of genus $ g $ and let $ (\alpha, \beta) $ be
a filling pair on $ S_g $; then $ i(\alpha, \beta) \geq 2g-1 $, where $ i $ is
the (geometric) intersection number. Aougab and Huang demonstrated that
(exponentially many) minimally-intersecting filling pairs exist on $ S_g $ when
$ g > 2 $ by a construction which produces higher-genus surfaces with filling
pairs as connected sums of lower-genus surfaces with filling pairs. We present
a generalization of their construction which provides an explicit, algebraic
means of determining the homeomorphism class of the resulting pair, and a
criterion for determining when a surface with minimally-intersecting filling
pair admits a decomposition as a connected sum.
