Vector-spread monomial ideals and Eliahou–Kervaire type resolutions.

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. [ABSTRACT FROM AUTHOR]