Stanley decompositions and Hilbert depth in the Koszul complex

DOI10.1216/JCA-2010-2-3-327zbMath1237.13026arXiv0909.0686OpenAlexW2962811147MaRDI QIDQ412506

Christian Krattenthaler, Jan Uliczka, Winfried Bruns

Publication date: 4 May 2012

Published in: Journal of Commutative Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.0686

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Syzygies, resolutions, complexes and commutative rings (13D02)

Related Items (20)

Hilbert depth of graded modules over polynomial rings in two variables ⋮ Four Generated, Squarefree, Monomial Ideals ⋮ How to compute the multigraded Hilbert depth of a module ⋮ Stanley depth of the integral closure of monomial ideals ⋮ On the Stanley depth of powers of edge ideals ⋮ A lower bound for depths of powers of edge ideals ⋮ Bounds on the Stanley depth and Stanley regularity of edge ideals of clutters ⋮ On the Stanley depth of powers of some classes of monomial ideals ⋮ The behavior of Stanley depth under polarization ⋮ Stanley depth and simplicial spanning trees ⋮ An algorithm to compute the Hilbert depth ⋮ Gröbner bases of syzygies and Stanley depth ⋮ The Stanley Depth in the Upper Half of the Koszul Complex ⋮ Betti posets and the Stanley depth ⋮ LINEAR QUOTIENTS AND MULTIGRADED SHIFTS OF BOREL IDEALS ⋮ How to compute the Stanley depth of a module ⋮ Hilbert series and Hilbert depth of squarefree Veronese ideals ⋮ When will the Stanley depth increase? ⋮ An Algorithm for Computing the Multigraded Hilbert Depth of a Module ⋮ The Stanley regularity of complete intersections and ideals of mixed products

Cites Work

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• Interval partitions and Stanley depth
• 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
• Combinatorial decompositions of a class of rings
• Determinantal rings
• Stanley depth of multigraded modules
• Stanley decompositions and partitionable simplicial complexes
• Some remarks on the Stanley's depth for multigraded modules
• Depth and Stanley Depth of Multigraded Modules

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