On the shape of a pure 𝑂-sequence

DOI10.1090/S0065-9266-2011-00647-7zbMath1312.13001arXiv1003.3825OpenAlexW4241483205MaRDI QIDQ5403719

Mats Boij, Fabrizio Zanello, Rosa Maria Miró-Roig, Juan C. Migliore, Uwe Nagel

Publication date: 18 March 2014

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.3825

zbMATH Keywords

enumerationGorenstein algebraunimodalityweak Lefschetz propertystrong Lefschetz propertyArtinian algebralevel algebramonomial algebradifferentiable \(O\)-sequencepure \(O\)-sequenceinterval conjectureMacaulay's inverse system\(g\)-elementmatroid simplicial complex

Mathematics Subject Classification ID

Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Combinatorics of partially ordered sets (06A07) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Combinatorial aspects of matroids and geometric lattices (05B35) Asymptotic enumeration (05A16) Commutative Artinian rings and modules, finite-dimensional algebras (13E10) Research exposition (monographs, survey articles) pertaining to commutative algebra (13-02) Combinatorial aspects of commutative algebra (05E40)

Related Items (27)

Equivariant Hilbert series in non-Noetherian polynomial rings ⋮ An algebraic approach to finite projective planes ⋮ The weak Lefschetz property for monomial ideals of small type ⋮ h-Vectors of Matroid Complexes ⋮ Generic and special constructions of pure O -sequences ⋮ On ideals with the Rees property ⋮ The unimodality of pure \(O\)-sequences of type three in three variables ⋮ \(f\)-vectors of pure complexes and pure multicomplexes of rank three ⋮ Generalized permutohedra, \(h\)-vectors of cotransversal matroids and pure \(O\)-sequences ⋮ Lagrangian geometry of matroids ⋮ Squeezed complexes ⋮ Forcing the weak Lefschetz property for equigenerated monomial ideals ⋮ Log-concave Gorenstein sequences ⋮ The Lefschetz properties of monomial complete intersections in positive characteristic ⋮ Arithmetically Cohen-Macaulay bundles and sets of points on general surfaces ⋮ Combinatorics and Algebra of Geometric Subdivision Operations ⋮ The strong Lefschetz property in codimension two ⋮ Hyperplane sections and the subtlety of the Lefschetz properties ⋮ Syzygy bundles and the weak Lefschetz property of monomial almost complete intersections ⋮ Maximal-clique partitions and the roller coaster conjecture ⋮ Artinian Level Algebras of Low Socle Degree ⋮ The Lefschetz question for ideals generated by powers of linear forms in few variables ⋮ Two unfortunate properties of pure $f$-vectors ⋮ Lexicographic shellability, matroids, and pure order ideals ⋮ Determinantal schemes and pure O-sequences ⋮ Unimodality of partitions with distinct parts inside Ferrers shapes ⋮ The unimodality of pure \(O\)-sequences of type two in four variables

Uses Software

• CoCoA
• Macaulay2

Cites Work

• Pure \(O\)-sequences and matroid \(h\)-vectors
• Trivariate monomial complete intersections and plane partitions
• On the structure of the \(h\)-vector of a paving matroid
• Monomial complete intersections, the weak Lefschetz property and plane partitions
• Classification algorithms for codes and designs
• A non-unimodal codimension 3 level \(h\)-vector
• Generic initial ideals and graded Artinian-level algebras not having the weak-Lefschetz property
• Glicci simplicial complexes
• Syzygy bundles on \(\mathbb P^2\) and the weak Lefschetz property
• Binomial determinants, paths, and hook length formulae
• What can be said about pure O-sequences?
• The number of \(M\)-sequences and \(f\)-vectors
• The number of faces of a simplicial convex polytope
• Eine Bedingung für die Flachheit und das Hilbertpolynom eines graduierten Ringes
• Hilbert functions of graded algebras
• \(g\)-elements of matroid complexes.
• Independence sequences of well-covered graphs: Non-unimodality and the roller-coaster conjecture
• Reduced arithmetically Gorenstein schemes and simplicial polytopes with maximal Betti numbers.
• Quaternionic geometry of matroids
• Another involution principle-free bijective proof of Stanley's hook-content formula
• Power sums, Gorenstein algebras, and determinantal loci. With an appendix `The Gotzmann theorems and the Hilbert scheme' by Anthony Iarrobino and Steven L. Kleiman
• The weak and strong Lefschetz properties for Artinian \(K\)-algebras
• Toric hyperkähler varieties
• Extending the idea of compressed algebra to arbitrary socle-vectors. II: Cases of non-existence
• Combinatorics and commutative algebra.
• Matroid inequalities
• The weak Lefschetz property, monomial ideals, and lozenges
• On the \(h\)-vector of a lattice path matroid
• Interval conjectures for level Hilbert functions
• Independence polynomials of well-covered graphs: generic counterexamples for the unimodality conjecture
• The finite free extension of Artinian \(K\)-algebras with the strong Lefschetz property
• Advanced determinant calculus: a complement
• The weak Lefschetz property for monomial ideals of small type
• Lifting monomial ideals
• Gorenstein liaison, complete intersection liaison invariants and unobstructedness
• Monomial ideals, almost complete intersections and the Weak Lefschetz property
• Compressed Algebras: Artin Algebras Having Given Socle Degrees and Maximal Length
• The Hilbert function of a level algebra
• On the degree two entry of a Gorenstein $h$-vector and a conjecture of Stanley
• The Geometry of the Weak Lefschetz Property and Level Sets of Points
• Strongly-MDS convolutional codes
• The unimodality conjecture for convex polytopes
• Weyl Groups, the Hard Lefschetz Theorem, and the Sperner Property
• On Complete Intersections and Their Hilbert Functions
• A nonunimodal graded gorenstein artin algebra in codimension five
• Roots of the Reliability Polynomials
• Nonunimodality of Graded Gorenstein Artin Algebras
• Graded gorenstein artin algebras whose hilbert functions have a large number of valleys
• Two Decompositions in Topological Combinatorics with Applications to Matroid Complexes
• CANCELLATION IN RESOLUTIONS AND LEVEL ALGEBRAS
• Level Algebras, Lex Segments, and Minimal Hilbert Functions
• Level algebras with bad properties
• Level Algebras of Type 2
• The Nonexistence of Certain Finite Projective Planes
• Theory of Matroids
• Hilbert functions and level algebras
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On the shape of a pure 𝑂-sequence