Nonexistence of exceptional imprimitive Q-polynomial association schemes with six classes

Authors:
Hajime Tanaka;Rie Tanaka
Affiliations:
-;-
Venue:
European Journal of Combinatorics
Year:
2011

Citing 5
Cited 0

Imprimitive Q-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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Abstract

Suzuki (1998) [9] showed that an imprimitive Q-polynomial association scheme with first multiplicity at least 3 is Q-bipartite, or is Q-antipodal, or has four or six classes. The exceptional case with four classes has recently been ruled out by Cerzo and Suzuki (2009) [5]. In this paper, we show the nonexistence of the last case with six classes. Hence Suzuki's theorem now exactly mirrors its well-known counterpart for imprimitive distance-regular graphs.