Stanley depth of complete intersection monomial ideals and upper-discrete partitions

AbstractLet I be an m-generated complete intersection monomial ideal in S=K[x1,…,xn]. We show that the Stanley depth of I is n−⌊m2⌋. We also study the upper-discrete structure for monomial ideals and prove that if I is a squarefree monomial ideal minimally generated by 3 elements, then the Stanley depth of I is n−1