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

Abstract

Let I be an m-generated complete intersection monomial ideal inWe 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.

Depth and Stanley depth of the edge ideals of square paths and square cycles

“…. , x n ] for some degrees [4,12], results on the Stanley depth of complete intersection monomial ideals [13,15,22], and CoCoA implementations of the algorithm [10,21].…”

Stanley depth of monomial ideals with small number of generators

“…If I ⊂ S is a monomial ideal, we are interested in computing sdepth(S/I) and sdepth(I). There are some papers regarding this problem, like [5,8,10,12,14]. Stanley's conjecture says that sdepth(S/I) ≥ depth(S/I), or in the general case, sdepth(M) ≥ depth(M), where M is a finitely generated multigraded S-module.…”

Alexander duality and Stanley depth of multigraded modules

“…While it is obvious that sdepth M dim S M, this invariant behaves somewhat strangely. For example, if I is a complete intersection monomial ideal of codimension c then we have sdepth(S/I) = n − c but sdepth I = n − c 2 as shown in [13]. The following is a special case of the conjecture raised in [15].…”

“…(See for example [6,7,13,14]. Here we listed papers directly related to the present paper, and there are many other interesting works.)…”