Vector-spread monomial ideals and Eliahou–Kervaire type resolutions

Abstract

We introduce the class of vector-spread monomial ideals. This notion generalizes that of t-spread ideals introduced by Ene, Herzog and Qureshi. In particular, we focus on vector-spread strongly stable ideals, we compute their Koszul cycles and describe their minimal free resolution. As a consequence the graded Betti numbers and the Poincaré series are determined. Finally, we consider a generalization of algebraic shifting theory for such a class of ideals.