Computing the support of monomial iterated mapping cones

In this paper we compute and manipulate the support of monomial resolutions based on iterated mapping cones. We derive in this way algorithms to obtain homological and numerical invariants of monomial ideals without actually computing their resolution. Our computations include Betti diagrams, Hilbert series and irreducible decompositions. The algorithms derived by the method presented in the paper are efficient in practice as shown by experiments.