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

Abstract

Let I be an m-generated complete intersection monomial ideal in S = K [ x 1 , … , x n ] . We show that the Stanley depth of I is n − ⌊ m 2 ⌋ . 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 .