Cohen-Macaulay ordered sets

DOI10.1016/0021-8693(80)90033-2zbMath0451.06004OpenAlexW2060557352WikidataQ89047169 ScholiaQ89047169MaRDI QIDQ1147726

Kenneth Baclawski

Publication date: 1980

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

Full work available at URL: https://doi.org/10.1016/0021-8693(80)90033-2

zbMATH Keywords

simplicial complexorder complexpartially ordered setsorder idealCohen-Macaulay posetbouquetmaximal subchains

Mathematics Subject Classification ID

Partial orders, general (06A06) Generalized (extraordinary) homology and cohomology theories in algebraic topology (55N20) Homotopy theory (55P99) Semimodular lattices, geometric lattices (06C10) Semilattices (06A12) Homological algebra in category theory, derived categories and functors (18G99)

Related Items (47)

Unnamed Item ⋮ Cohen-Macaulay rings of sections ⋮ A shellable poset that is not lexicographically shellable ⋮ A non-partitionable Cohen-Macaulay simplicial complex ⋮ Stanley-Reisner Rings ⋮ The homology of partitions with an even number of blocks ⋮ For Which Finite Groups G is the Lattice ℒ(G) of Subgroups Gorenstein? ⋮ A homological fibration for \(Gl_\infty\) ⋮ Level rings and algebras with straightening laws ⋮ Union and glueing of a family of Cohen-Macaulay partially ordered sets ⋮ Canonical homeomorphisms of posets ⋮ Bruhat order on the involutions of classical Weyl groups. ⋮ Posets for which Verdier duality holds ⋮ On the homology of the noncrossing partition lattice and the Milnor fibre ⋮ Categorifications of rational Hilbert series and characters of \(\boldsymbol{FS}^{\mathrm{op}}\) modules ⋮ The Bruhat Order of the Symmetric Group is Lexicographically Shellable ⋮ Combinatorial methods in the theory of Cohen-Macaulay rings ⋮ Combinatorial decompositions of a class of rings ⋮ Rings with lexicographic straightening law ⋮ The Bruhat order on the involutions of the hyperoctahedral group. ⋮ On the number of faces of simplicial complexes and the purity of Frobenius ⋮ On Quillen's theorem A for posets ⋮ A poset fiber theorem for doubly Cohen-Macaulay posets and its applications. ⋮ Some aspects of groups acting on finite posets ⋮ A quasi Curtis-Tits-Phan theorem for the symplectic group. ⋮ Decomposition theorem for the cd-index of Gorenstein posets ⋮ Fixed points in partially ordered sets ⋮ Cohen-Macaulay Section Rings ⋮ Poset fiber theorems ⋮ Modules of piecewise polynomials and their freeness ⋮ Canonical ideals of Cohen-Macaulay partially ordered sets ⋮ A dualizing complex for Stanley–Reisner rings ⋮ Bruhat order on classical Weyl groups: minimal chains and covering relation. ⋮ Spectral sequences on combinatorial simplicial complexes ⋮ Segre and Rees products of posets, with ring-theoretic applications ⋮ Galois connections and the Leray spectral sequence ⋮ Some properties of the parking function poset ⋮ Unnamed Item ⋮ A Curtis-Tits-Phan theorem for the twin-building of type \(A_{n-1}\) ⋮ Quotients of Coxeter complexes and buildings with linear diagram ⋮ Cohen-Macaulay connectivity and geometric lattices ⋮ From graphs to ortholattices and equivariant maps ⋮ Homotopy of non-modular partitions and the Whitehouse module ⋮ Combinatorial decompositions of rings and almost Cohen-Macaulay complexes ⋮ Generalized Dehn-Sommerville relations for polytopes, spheres and Eulerian partially ordered sets ⋮ The lexicographic sum of Cohen-Macaulay and shellable ordered sets ⋮ The split building of a reductive group

Cites Work

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• Combinatorial decompositions of a class of rings
• Finite lattices and Jordan-Hölder sets
• Whitney numbers of geometric lattices
• Cohen-Macaulay quotients of polynomial rings
• Galois connections and the Leray spectral sequence
• Homotopy properties of the poset of nontrivial p-subgroups of a group
• The Grothendieck-Cousin complex of an induced representation
• The Möbius algebra as a Grothendieck ring
• Modular elements of geometric lattices
• Supersolvable lattices
• An unshellable triangulation of a tetrahedron
• The Upper Bound Conjecture and Cohen-Macaulay Rings
• Which Spheres are Shellable?
• Balanced Cohen-Macaulay Complexes
• The Möbius function of a lattice
• Schemes with Finite-Dimensional Cohomology Groups
• Shellable Decompositions of Cells and Spheres.
• [https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]
• Fixed points in partially ordered sets
• Combinatorial reciprocity theorems

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