TY - JOUR
T1 - Nonexistence of exceptional imprimitive Q-polynomial association schemes with six classes
AU - Tanaka, Hajime
AU - Tanaka, Rie
N1 - Funding Information:
RT would like to thank Akihiro Munemasa for discussions and encouragement. HT is supported by the JSPS Excellent Young Researchers Overseas Visit Program .
PY - 2011/2
Y1 - 2011/2
N2 - 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.
AB - 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.
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U2 - 10.1016/j.ejc.2010.09.006
DO - 10.1016/j.ejc.2010.09.006
M3 - Article
AN - SCOPUS:78049514371
SN - 0195-6698
VL - 32
SP - 155
EP - 161
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
IS - 2
ER -