Extremal Betti numbers of t-spread strongly stable ideals

Let K be a field and let S = K[x_1, . . . , x_n] be a polynomial ring over K. We analyze the extremal Betti numbers of special squarefree monomial ideals of S known as the t-spread strongly stable ideals, where t is an integer grater than or equal to 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 ideals with the maximal number of extremal Betti numbers when t = 2.