On the Stanley depth of weakly polymatroidal ideals

摘要

Let K be a field and S = K[x_1,...,x_n] be the polynomial ring in n variables over the field K. In this paper, it is shown that Stanley's conjecture holds for I and S/I if I is a product of monomial prime ideals or I is a high enough power of a polymatroidal or a stable ideal generated in a single degree.