Stanley depth and size of a monomial ideal
arXiv:1011.6462
Abstract
Lyubeznik introduced the concept of size of a monomial ideal and showed that the size of a monomial ideal increased by is a lower bound for its depth. We show that the size is also a lower bound for its Stanley depth. Applying Alexander duality we obtain upper bounds for the regularity and Stanley regularity of squarefree monomial ideals.