The distance spectra of Cayley graphs of Coxeter groups

DOI10.1016/j.disc.2011.01.021zbMath1233.05132OpenAlexW2166190372MaRDI QIDQ533786

Paul Renteln

Publication date: 6 May 2011

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2011.01.021

zbMATH Keywords

Cayley graphCoxeter groupBruhat orderdistance matrixdistance spectrumabsolute order graphdistance polynomialweak order graph

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Distance in graphs (05C12)

Related Items

Distance-integral Cayley graphs over abelian groups and dicyclic groups ⋮ On Cayley graphs over generalized dicyclic groups ⋮ Eigenvalues of Cayley graphs ⋮ Diagonalization of matrices of statistics ⋮ Spectrum of Cayley graphs on the symmetric group generated by transpositions ⋮ A natural idempotent in the descent algebra of a finite Coxeter group ⋮ On the eigenvalues of certain Cayley graphs and arrangement graphs ⋮ Remarks on D-integral complete multipartite graphs ⋮ Catalogue of the Star graph eigenvalue multiplicities ⋮ \(PI\)-eigenfunctions of the Star graphs ⋮ Integral and distance integral Cayley graphs over generalized dihedral groups ⋮ Spectra of Cayley graphs of complex reflection groups ⋮ Spectra of Symmetrized Shuffling Operators ⋮ Distance integral generalized wheel graphs ⋮ On distance integral graphs ⋮ The intermediate orders of a Coxeter group

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Poincaré polynomials of representations of finite groups generated by reflections
• Intersecting families in the alternating group and direct product of symmetric groups
• On the spectrum of the derangement graph
• Random shuffles and group representations
• Realizability of a model in infinite statistics
• Distance matrix polynomials of trees
• Factoring distance matrix polynomials
• Minimal eigenvalue of the Coxeter Laplacian for the symmetric group
• Bilinear form of real configuration of hyperplanes
• On the eigenvalues of the Coxeter Laplacian.
• Combinatorics of Coxeter Groups
• Distance spectrum of graph compositions
• Buildings
• Generalized noncrossing partitions and combinatorics of Coxeter groups
• Matrix Analysis
• A group-theoretic model for symmetric interconnection networks
• Generating a random permutation with random transpositions
• A $q$-deformation of a trivial symmetric group action
• The Fixed-Point-Space Dimension Function for a Finite Group Representation
• Invariants of Finite Reflection Groups
• Finite Unitary Reflection Groups
• Reflection groups and invariant theory