Sequentially Cohen-Macaulay monomial ideals of embedding dimension four

Abstract

Let $I$ be a monomial ideal of the polynomial ring $S=K[x_1,...,x_4]$ over a field $K$. Then $S/I$ is sequentially Cohen-Macaulay if and only if $S/I$ is pretty clean. In particular, if $S/I$ is sequentially Cohen-Macaulay then $I$ is a Stanley ideal.

11 pages

References in corpus (2)

• Criterions for Shellable Multicomplexes
• Stanley decompositions and partitionable simplicial complexes

Cited by in corpus (9)

• Stanley Conjecture in small embedding dimension
• Stanley depth of complete intersection monomial ideals
• Stanley depth of monomial ideals with small number of generators
• Stanley decompositions and localization
• Stanley depth of monomial ideals in three variables
• Stanley decompositions of squarefree modules and Alexander duality
• Stanley Depth of Multigraded Modules
• A note on Stanley conjecture for monomial ideals
• Stanley Decompositions and Polarization