Extremal Betti Numbers of t-Spread Strongly Stable Ideals

Abstract

Let K be a field and let S = K[x1, . . . , xn] be a polynomial ring over K. We analyze the extremal Betti numbers of special squarefree monomial ideals of S known as the t-spread stronglystable ideals, where t is an integer ≥ 1. A characterization of the extremal Betti numbers of such a class of ideals is given. Moreover, we determine the structure of the t-spread strongly stable idealswith the maximal number of extremal Betti numbers when t = 2.