Posets that locally resemble distributive lattices. An extension of Stanley's theorem (with connections to buildings and diagram geometries)

DOI10.1006/jcta.1999.3049zbMath0967.06003OpenAlexW1987554631MaRDI QIDQ1841221

Jonathan David Farley, Stefan E. Schmidt

Publication date: 27 June 2001

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcta.1999.3049

zbMATH Keywords

projective spacediagram geometrymodular latticessemimodular latticedistributive latticegraded posetincidence geometryBoolean latticesproducts of chainstheory of buildings

Mathematics Subject Classification ID

Combinatorics of partially ordered sets (06A07) Buildings and the geometry of diagrams (51E24) Structure and representation theory of distributive lattices (06D05) Semimodular lattices, geometric lattices (06C10) Complemented lattices, orthocomplemented lattices and posets (06C15) Modular lattices, Desarguesian lattices (06C05)

Related Items (6)

Classification of the factorial functions of Eulerian binomial and Sheffer posets ⋮ Chain decomposition and the flag \(f\)-vector. ⋮ Finite Eulerian posets which are binomial, Sheffer or triangular ⋮ Distributive lattices of small width. II: A problem from Stanley's 1986 text \textsl{Enumerative combinatorics} ⋮ Posets in which every interval is a product of chains, and natural local actions of the symmetric group ⋮ Flag-symmetry of the poset of shuffles and a local action of the symmetric group

Cites Work

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• Finite free resolutions and 1-skeletons of simplicial complexes
• Some combinatorial and algebraic properties of Coxeter complexes and Tits buildings
• Diagrams for geometries and groups
• Whitney numbers of the second kind of finite modular lattices
• Posets in which every interval is a product of chains, and natural local actions of the symmetric group
• The comparability graph of a modular lattice
• Quotients of Coxeter complexes and buildings with linear diagram
• The dimension theorem in axiomatic geometry
• Flag-symmetric and locally rank-symmetric partially ordered sets
• Semimodular Posets and the Jordan-Dedekind Chain Condition

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