Imprimitive cometric association schemes: Constructions and analysis

Authors:
William J. Martin;Mikhail Muzychuk;Jason Williford
Affiliations:
Department of Mathematical Sciences and Department of Computer Science, Worcester Polytechnic Institute, Worcester, USA;Department of Computer Science and Mathematics, Netanya Academic College, Netanya, Israel 42365;Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, USA
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2007

Citing 5
Cited 10

The Subconstituent Algebra of an Association Scheme, (Part I)

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Imprimitive Q-polynomial Association Schemes

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Three-Class Association Schemes

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Association Schemes Related to Kasami Codes and KerdockSets

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Width and dual width of subsets in polynomial association schemes

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Non-existence of imprimitive Q-polynomial schemes of exceptional type with d=4

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

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A survey on spherical designs and algebraic combinatorics on spheres

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Commutative association schemes

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On the equivalence between real mutually unbiased bases and a certain class of association schemes

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Coherent configurations and triply regular association schemes obtained from spherical designs

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New families of Q-polynomial association schemes

Journal of Combinatorial Theory Series A
A characterization of Q-polynomial association schemes

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Bounds on s-Distance Sets with Strength t

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Linking systems in nonelementary abelian groups

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Abstract

Dualizing the "extended bipartite double" construction for distance-regular graphs, we construct a new family of cometric (or Q-polynomial) association schemes with four associate classes based on linked systems of symmetric designs. The analysis of these new schemes naturally leads to structural questions concerning imprimitive cometric association schemes, some of which we answer with others being left as open problems. In particular, we prove that any Q-antipodal association scheme is dismantlable: the configuration induced on any subset of the equivalence classes in the Q-antipodal imprimitivity system is again a cometric association scheme. Further examples are explored.