Quotients of Coxeter complexes and buildings with linear diagram

DOI10.1016/S0195-6698(86)80019-1zbMath0616.51009OpenAlexW2031547052MaRDI QIDQ1821349

Michelle L. Wachs

Publication date: 1986

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0195-6698(86)80019-1

zbMATH Keywords

Coxeter groupshellabilityquotient buildingsquotient Coxeter complexes

Mathematics Subject Classification ID

Partial orders, general (06A06) Finite geometry and special incidence structures (51E99) Designs and configurations (05B99) General convexity (52A99)

Related Items

A shellable poset that is not lexicographically shellable, Group actions on Stanley-Reisner rings and invariants of permutation groups, Posets that locally resemble distributive lattices. An extension of Stanley's theorem (with connections to buildings and diagram geometries)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some combinatorial and algebraic properties of Coxeter complexes and Tits buildings
• A characterization of Kempf varieties by means of standard monomials and the geometric consequences
• Cohen-Macaulay ordered sets
• Combinatorial methods in the theory of Cohen-Macaulay rings
• Bruhat order of Coxeter groups and shellability
• Combinatorial maps
• Reflection compound representations of groups of type A//n,B//n or \(C_ n\).
• Buildings of spherical type and finite BN-pairs
• Some characterizations of Bruhat ordering on a Coxeter group and determination of the relation Möbius function
• Group actions on Stanley-Reisner rings and invariants of permutation groups
• On Lexicographically Shellable Posets
• Shellable and Cohen-Macaulay Partially Ordered Sets
• Weyl Groups, the Hard Lefschetz Theorem, and the Sperner Property
• The Complete Enumeration of Finite Groups of the Form Ri2=(RiRj)kij=1
• Möbius inversion for the Bruhat ordering on a Weyl group