Monomial complete intersections, the weak Lefschetz property and plane partitions

DOI10.1016/j.disc.2010.09.006zbMath1202.13013arXiv1002.4400OpenAlexW1976018363MaRDI QIDQ607018

Sumit K. Garg

Publication date: 19 November 2010

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

Full work available at URL: https://arxiv.org/abs/1002.4400

zbMATH Keywords

complete intersectionsmonomial algebrasplane partitionsweak Lefschetz propertycharacteristic pdeterminant evaluations

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial aspects of partitions of integers (05A17) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Complete intersections (14M10)

Related Items

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 minimal number of generators of a Togliatti system ⋮ Trivariate monomial complete intersections and plane partitions ⋮ The weak Lefschetz property of Gorenstein algebras of codimension three associated to the Apéry sets ⋮ Forcing the weak Lefschetz property for equigenerated monomial ideals ⋮ A note on the weak Lefschetz property of monomial complete intersections in positive characteristic ⋮ The Lefschetz properties of monomial complete intersections in positive characteristic ⋮ The resolution of the bracket powers of the maximal ideal in a diagonal hypersurface ring ⋮ On the weak Lefschetz property for vector bundles on \(\mathbb{P}^2\) ⋮ Globally generated vector bundles and the weak Lefschetz property ⋮ The strong Lefschetz property in codimension two ⋮ Hyperplane sections and the subtlety of the Lefschetz properties ⋮ On the degrees of relations on \(x_1^{d_1}, \dots, x_n^{d_n},(x_1 + \dots + x_n)^{d_{n + 1}}\) in positive characteristic ⋮ Syzygy bundles and the weak Lefschetz property of monomial almost complete intersections ⋮ On the shape of a pure 𝑂-sequence ⋮ On the structure of monomial complete intersections in positive characteristic ⋮ On the weak Lefschetz property for artinian Gorenstein algebras of codimension three ⋮ The Lefschetz question for ideals generated by powers of linear forms in few variables ⋮ A note on a conjecture regarding the weak Lefschetz property of a special class of Artinian algebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Partition bijections, a survey
• The Hilbert functions which force the Weak Lefschetz property
• The determinants of certain matrices arising from the Boolean lattice
• Forcing the strong Lefschetz and the maximal rank properties
• Hilbert functions of graded algebras
• Advanced determinant calculus
• Another involution principle-free bijective proof of Stanley's hook-content formula
• The weak and strong Lefschetz properties for Artinian \(K\)-algebras
• A bijection between classes of fully packed loops and plane partitions
• Overlapping Pfaffians
• 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
• The Problem of the Calissons
• On Complete Intersections and Their Hilbert Functions

This page was built for publication: Monomial complete intersections, the weak Lefschetz property and plane partitions