Trivariate monomial complete intersections and plane partitions

DOI10.1216/JCA-2011-3-4-459zbMath1236.05212arXiv1008.1426OpenAlexW2964140444MaRDI QIDQ412559

Charles P. Chen, Alan Guo, Gaku Liu, Xin Jin

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/1008.1426

zbMATH Keywords

Toeplitz matrixhomogeneous componentsSchur polynomialsSmith normal forms

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Determinants, permanents, traces, other special matrix functions (15A15) Commutative Artinian rings and modules, finite-dimensional algebras (13E10) Group actions on combinatorial structures (05E18) Combinatorial aspects of commutative algebra (05E40)

Related Items (8)

An algebraic approach to finite projective planes ⋮ The weak Lefschetz property for monomial ideals of small type ⋮ The Weak Lefschetz Property for monomial complete intersection in positive characteristic ⋮ The Lefschetz properties of monomial complete intersections in positive characteristic ⋮ Syzygy bundles and the weak Lefschetz property of monomial almost complete intersections ⋮ On the shape of a pure 𝑂-sequence ⋮ Signed lozenge tilings ⋮ On the weak Lefschetz property for artinian Gorenstein algebras of codimension three

Cites Work

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• Monomial complete intersections, the weak Lefschetz property and plane partitions
• The Hilbert functions which force the Weak Lefschetz property
• The determinants of certain matrices arising from the Boolean lattice
• An exploration of the permanent-determinant method
• Symmetries of plane partitions and the permanent-determinant method
• Kasteleyn cokernels
• A diagonal form for the incidence matrices of \(t\)-subsets vs. \(k\)- subsets
• The weak Lefschetz property, monomial ideals, and lozenges
• A note on the weak Lefschetz property of monomial complete intersections in positive characteristic
• Monomial ideals, almost complete intersections and the Weak Lefschetz property

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