A numerical semigroup
is an additively closed set of nonnegative integers, and a factorization of an element
of
is an expression
of
as a sum of
generators of
.
It is known that for a given numerical semigroup
, the number of
factorizations of
coincides with a quasipolynomial (that is, a polynomial whose coefficients are periodic
functions of
).
One of the standard methods for computing certain semigroup-theoretic invariants
involves assembling a graph or simplicial complex derived from the factorizations of
. We
prove that for two such graphs (which we call the factorization support graph and the
trade graph), the number of edges coincides with a quasipolynomial function of
, and
identify the degree, period, and leading coefficient of each. In the process, we uncover
a surprising geometric connection: a combinatorially assembled cubical complex that
is homeomorphic to real projective space.
