Stanley depth of squarefree monomial ideals

In this paper, we answer a question posed by Y.H. Shen. We prove that if I is an m-generated squarefree monomial ideal in the polynomial ring S=K[x1,…,xn] with K a field, then sdepthI⩾n−⌊m/2⌋. The proof is inductive and uses the correspondence between a Stanley decomposition of a monomial ideal and a partition of a particular poset into intervals established by Herzog, Vladoiu and Zheng.