Minimal free resolutions of certain equigenerated monomial ideals

Let R=k[x1,…,xn] denote the standard graded polynomial ring over a field k. We study certain classes of equigenerated monomial ideals with property that so-called complementary ideal has no linear relations on generators. then use iterated trimming complexes to deduce Betti numbers for such ideals. Furthermore, using result splitting mapping cones by Miller and Rahmati, we construct minimal free resolutions all under consideration explicitly conclude questions about extra structure these complexes.