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arXiv · 1311.5942

Nonexistence of Exceptional 5-class Association Schemes with Two $Q$-polynomial Structures

Jianmin Ma·Kaishun Wang
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Abstract

In [H. Suzuki, Association schemes with multiple $Q$-polynomial structures, J. Algebraic Combin. 7 (1998) 181-196], Suzuki gave a classification of association schemes with multiple $Q$-polynomial structures, allowing for one exceptional case which has five classes. In this paper, we rule out the existence of this case. Hence Suzuki's theorem mirrors exactly the well-known counterpart for association schemes with multiple $P$-polynomial structures, a result due to Eiichi Bannai and Etsuko Bannai in 1980.

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Jianmin Ma, Kaishun Wang. 2013-11-23. Nonexistence of Exceptional 5-class Association Schemes with Two $Q$-polynomial Structures. https://arxiv.org/abs/1311.5942

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