Betti numbers of modules of essentially monomial type

Let R be a Noetherian local ring. In this paper we supply formulae for computing the ranks of syzygy and Betti numbers of R-modules of essentially monomial type. These modules are defined with respect to various R-regular sequences. For example, finite length modules of monomial type over regular local rings of dimension n are modules of essentially monomial type with respect to R-regular sequences of length n. If a module is of essentially monomial type with respect to an R-regular sequence of length n, then the rank of its i-th syzygy is at least ((n-1)(i-1)) and its i-th Betti number is at least ((n)(i)).