Stanley depth of factors of polymatroidal ideals and the edge ideal of forests

摘要

Let be the polynomial ring in n variables over the field . Suppose that are polymatroidal ideals of S. We provide a lower bound for the Stanley depth of I/J. Using this lower bound, we prove that for every integer . We also prove that if I is the edge ideal of a forest graph with p connected components, then and conclude that for every integer k 0 .