An Algorithm for Computing the Multigraded Hilbert Depth of a Module

DOI10.1080/10586458.2014.908753zbMath1312.13024arXiv1304.7215OpenAlexW2089738413MaRDI QIDQ5249308

Andrei Zarojanu, Bogdan Ichim

Publication date: 30 April 2015

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.7215

zbMATH Keywords

computational experimentsStanley depthHilbert depth

Mathematics Subject Classification ID

Computational aspects and applications of commutative rings (13P99) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Theory of modules and ideals in commutative rings (13C99) Combinatorial aspects of commutative algebra (05E40)

Related Items (8)

A non-partitionable Cohen-Macaulay simplicial complex ⋮ Four Generated, Squarefree, Monomial Ideals ⋮ Combinatorial reductions for the Stanley depth of \(I\) and \(S/I\) ⋮ Stanley depth and simplicial spanning trees ⋮ Betti posets and the Stanley depth ⋮ LCM Lattices and Stanley Depth: A First Computational Approach ⋮ Unnamed Item ⋮ How to compute the Stanley depth of a module

Uses Software

• CoCoA
• Hdepth

Cites Work

• Unnamed Item
• Stanley decompositions and Hilbert depth in the Koszul complex
• Normaliz: Algorithms for affine monoids and rational cones
• Finite filtrations of modules and shellable multicomplexes
• Remarks on Hilbert series of graded modules over polynomial rings
• Stanley depth of complete intersection monomial ideals and upper-discrete partitions
• Linear Diophantine equations and local cohomology
• The Alexander duality functors and local duality with monomial support
• On a conjecture of R. P. Stanley. I: Monomial ideals
• On a conjecture of R. P. Stanley. II: Quotients modulo monomial ideals
• An algorithm to compute the Hilbert depth
• Hilbert depth of graded modules over polynomial rings in two variables
• 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
• How to compute the multigraded Hilbert depth of a module
• Polytopes, Rings, and K-Theory
• A Survey on Stanley Depth

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