  Let $R = k[x_1, \dotsc , x_n]$ denote the standard graded polynomial ring
over a field $k$. We study certain classes of equigenerated monomial ideals
with the property that the so-called complementary ideal has no linear
relations on the generators. We then use iterated trimming complexes to deduce
Betti numbers for such ideals. Furthermore, using a result on splitting mapping
cones by Miller and Rahmati, we construct the minimal free resolutions for all
ideals under consideration explicitly and conclude with questions about extra
structure on these complexes.
