Some formulas for spin models on distance-regular graphs

zbMath0930.05101MaRDI QIDQ1305530

Nomura, Kazumasa, Curtin, Brian

Publication date: 9 February 2000

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

zbMATH Keywords

distance-regular graphassociation schemeBose-Mesner algebraspin modelsquare matrixinvariant of knots and links

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30)

Related Items

Spin Leonard pairs, Homogeneity of a distance-regular graph which supports a spin model, Compatibility and companions for Leonard pairs, Modular Leonard triples, Near-bipartite Leonard pairs, Leonard triples of \(q\)-Racah type and their pseudo intertwiners, Leonard pairs, spin models, and distance-regular graphs, Spin models and strongly hyper-self-dual Bose-Mesner algebras, Tridiagonal pairs of \(q\)-Racah-type and the \(q\)-tetrahedron algebra, The Terwilliger algebra of a distance-regular graph that supports a spin model, Spin models and Bose-Mesner algebras, Distance-regular graphs which support a spin model are thin, Modular invariance property of association schemes, type II codes over finite rings and finite abelian groups and reminiscences of François Jaeger (a survey), The Terwilliger algebra of a 2-homogeneous bipartite distance-regular graph

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An algebra associated with a spin model
• On knot invariants related to some statistical mechanical models
• Characterization of H(n,q) by the parameters
• Strongly regular graphs and spin models for the Kauffman polynomial
• Duality maps of finite abelian groups and their applications to spin models
• Bose-Mesner algebras related to type II matrices and spin models
• Distance-regular graphs which support a spin model are thin
• Spin models for link polynomials, strongly regular graphs and Jaeger's Higman-Sims model
• Spin models on finite cyclic groups
• New constructions of models for link invariants
• On spin models, modular invariance, and duality
• 2-homogeneous bipartite distance-regular graphs
• On spin models, triply regular association schemes, and duality
• A matrix equation for association schemes
• Kite-free distance-regular graphs
• Spin models on bipartite distance-regular graphs
• Modular invariance property and spin models attached to cyclic group association schemes
• Generalized generalized spin models (four-weight spin models)
• Spin models on triangle-free connected graphs
• CLASSIFICATION OF SMALL SPIN MODELS
• GENERALIZED SPIN MODELS
• On the uniqueness of a certain thin near octagon (or partial 2-geometry, or parallelism) derived from the binary Golay code
• Spin models constructed from Hadamard matrices
• Some classes of four-weight spin models