There are finitely many \(Q\)-polynomial association schemes with given first multiplicity at least three

DOI10.1016/j.ejc.2008.07.009zbMath1169.05054OpenAlexW2150308403MaRDI QIDQ1011512

Jason S. Williford, William J. Martin

Publication date: 8 April 2009

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

Full work available at URL: https://doi.org/10.1016/j.ejc.2008.07.009

zbMATH Keywords

distance regular graphsQ-polynomial association schemesrank of firts idempotent

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30)

Related Items (12)

Rationality of the inner products of spherical \(s\)-distance \(t\)-designs for \(t \geq 2s - 2\), \(s \geq 3\) ⋮ Classification of partially metric Q-polynomial association schemes with \(m_1=4\) ⋮ Nonexistence of exceptional imprimitive \(Q\)-polynomial association schemes with six classes ⋮ On the connectivity of graphs in association schemes ⋮ A characterization of \(Q\)-polynomial association schemes ⋮ There are only finitely many distance-regular graphs of fixed valency greater than two ⋮ On few-class Q-polynomial association schemes: feasible parameters and nonexistence results ⋮ Universal lower bounds for potential energy of spherical codes ⋮ Spherical embeddings of symmetric association schemes in 3-dimensional Euclidean space ⋮ A survey on spherical designs and algebraic combinatorics on spheres ⋮ Commutative association schemes ⋮ On the ideal of the shortest vectors in the Leech lattice and other lattices

Cites Work

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• Imprimitive cometric association schemes: constructions and analysis
• Bounding the diameter of distance. Regular graphs
• Eigenvalue multiplicities of highly symmetric graphs
• Splitting fields of association schemes
• Spherical codes and designs
• Problems in algebraic combinatorics
• Imprimitive Q-polynomial association schemes
• Association schemes with multiple Q-polynomial structures
• There are finitely many triangle-free distance-regular graphs with degree 8, 9 or 10
• Two theorems concerning the Bannai-Ito conjecture

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