Cayley lattices of finite Coxeter groups are bounded

DOI10.1016/j.aam.2003.09.002zbMath1097.06001OpenAlexW2081137745MaRDI QIDQ1883394

Nathalie Caspard, Claude Le Conte de Poly-Barbut, Michel Morvan

Publication date: 12 October 2004

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2003.09.002

zbMATH Keywords

Coxeter groupReflectionCoxeter latticeZonotopeBounded latticeDoubling operationSemidistributivity

Mathematics Subject Classification ID

Combinatorics of partially ordered sets (06A07) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Structure theory of lattices (06B05)

Related Items (17)

Congruence normality of simplicial hyperplane arrangements via oriented matroids ⋮ Three Fuss-Catalan posets in interaction and their associative algebras ⋮ Lattices of regular closed subsets of closure spaces ⋮ Derived semidistributive lattices ⋮ Lattice homomorphisms between weak orders ⋮ Sublattices of associahedra and permutohedra ⋮ Crosscut-simplicial lattices ⋮ The extended permutohedron on a transitive binary relation. ⋮ The order dimension of the poset of regions in a hyperplane arrangement. ⋮ On the join dependency relation in multinomial lattices ⋮ Lattice structure of grid-Tamari orders ⋮ Lattice congruences, fans and Hopf algebras. ⋮ Lattice structure of Weyl groups via representation theory of preprojective algebras ⋮ Cambrian lattices. ⋮ Sortable elements in infinite Coxeter groups ⋮ Minimal inclusions of torsion classes ⋮ Lattice congruences of the weak order.

Cites Work

• Subdirect decomposition of concept lattices
• Doubling convex sets in lattices and a generalized semidistributivity condition
• Congruence normality: The characterization of the doubling class of convex sets
• The generalized doubling construction and formal concept analysis
• The classification of zonohedra by means of projective diagrams
• Generalized Quotients in Coxeter Groups
• Characterizations of Finite Lattices that are Bounded-Homomqrphic Images or Sublattices of Free Lattices
• THE LATTICE OF PERMUTATIONS IS BOUNDED
• A Simple Solution to the Word Problem for Lattices
• Equational Bases and Nonmodular Lattice Varieties
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