A duality between pairs of split decompositions for a Q-polynomial distance-regular graph

DOI10.1016/j.disc.2010.01.004zbMath1231.05299arXiv0705.0167OpenAlexW2037247872MaRDI QIDQ973163

Joohyung Kim

Publication date: 28 May 2010

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

Full work available at URL: https://arxiv.org/abs/0705.0167

zbMATH Keywords

distance-regular graphsubconstituent algebrasplit decompositiontridiagonal pair

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Distance in graphs (05C12)

Related Items (4)

A \(Q\)-polynomial structure associated with the projective geometry \(L_N (q)\) ⋮ An action of the tetrahedron algebra on the standard module for the Hamming graphs and Doob graphs ⋮ Distance-regular graphs of \(q\)-Racah type and the \(q\)-tetrahedron algebra ⋮ Hypercube and tetrahedron algebra

Cites Work

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• The subconstituent algebra of an association scheme. I
• The subconstituent algebra of an association scheme. III
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• Distance-regular graphs and the \(q\)-tetrahedron algebra
• Spectra of bipartite \(P\)- and \(Q\)-polynomial association schemes
• The Terwilliger algebras of bipartite \(P\)- and \(Q\)-polynomial schemes
• Bipartite distance-regular graphs. I
• Problems in algebraic combinatorics
• Tight distance-regular graphs and the subconstituent algebra
• On the multiplicities of the primitive idempotents of a \(Q\)-polynomial distance-regular graph
• Tridiagonal pairs and the quantum affine algebra \(U_q(\widehat{\text{sl}}_2)\).
• The displacement and split decompositions for a \(Q\)-polynomial distance-regular graph
• Tight distance-regular graphs and the \(Q\)-polynomial property

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