On a Conjecture of Stanley Depth of Squarefree Veronese Ideals

DOI10.1080/00927872.2011.585190zbMath1261.13014arXiv0911.5458OpenAlexW2075052912MaRDI QIDQ3164934

Maorong Ge, Yi-Huang Shen, Jiayuan Lin

Publication date: 18 October 2012

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.5458

zbMATH Keywords

Stanley depthsquarefree monomial idealinterval partitionsquarefree Veronese ideal

Mathematics Subject Classification ID

Combinatorics of partially ordered sets (06A07) Algebraic combinatorics (05E99) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Algebraic aspects of posets (06A11) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15) Other special types of modules and ideals in commutative rings (13C13)

Related Items (4)

Combinatorial reductions for the Stanley depth of \(I\) and \(S/I\) ⋮ A variant of the Stanley depth for multisets ⋮ Gröbner bases of syzygies and Stanley depth ⋮ Hilbert series and Hilbert depth of squarefree Veronese ideals

Cites Work

• A lower bound of Stanley depth of monomial ideals
• On the Stanley depth of squarefree Veronese ideals
• Interval partitions and Stanley depth
• Stanley depth of complete intersection monomial ideals and upper-discrete partitions
• Linear Diophantine equations and local cohomology
• On a conjecture of R. P. Stanley. I: Monomial ideals
• On a conjecture of R. P. Stanley. II: Quotients modulo monomial ideals
• Cohen-Macaulay polymatroidal ideals
• Prime filtrations of monomial ideals and polarizations
• Stanley depth of multigraded modules
• Stanley decompositions and partitionable simplicial complexes
• Stanley conjecture in small embedding dimension
• How to compute the Stanley depth of a monomial ideal
• Stanley depth of squarefree monomial ideals

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