On stability properties of powers of polymatroidal ideals

摘要

Let R = K[x(1), ..., x(n)] be the polynomial ring in n variables over a field K with themaximal ideal m = (x(1), ..., x(n)). Let astab(I) and dstab(I) be the smallest integer n for which Ass(I n) and depth(I n) stabilize, respectively. In this paper we show that astab(I) = dstab(I) in the following cases: