Stanley depth of monomial ideals in three variables

Abstract

We show that $\depth(S/I)=0$ if and only if $\sdepth(S/I)=0$, where $I\subset S=K[x_1,...,x_n]$ is a monomial ideal. We give an algorithm to compute the Stanley depth of $S/I$, where $I\subset S=K[x_1,x_2,x_3]$ is a monomial ideal. Also, we prove that a monomial ideal $I\subset K[x_1,x_2,x_3]$ minimally generated by three monomials has $\sdepth(I)=2$.

9 pages

References in corpus (6)

• Stanley Conjecture in small embedding dimension
• Stanley depth of complete intersection monomial ideals
• Stanley Decompositions, Pretty Clean Filtrations and Reductions Modulo Regular Elements
• Stanley decompositions and localization
• Sequentially Cohen-Macaulay monomial ideals of embedding dimension four
• Stanley depth of complete intersection monomial ideals and upper-discrete partitions

Cited by in corpus (6)

• An inequality between depth and Stanley depth
• Stanley decompositions and localization
• Some remarks on the Stanley's depth for multigraded modules
• Stanley's conjecture for critical ideals
• Computing the Stanley depth
• Depth and Stanley depth of multigraded modules