Annals of Combinatorics 4 (2000) 139-151
The Classification of Certain Four-Weight Spin Models
Etsuko Bannai and Mitsuhiro Sawano
Graduate School of Mathematics, Kyushu University, 6-10-1 Hakozaki,
Higashi-ku, Fukuoka 812-8581, Japan
Received March 27, 1999
AMS Subject Classification: 05E30, 05E99
Abstract. In this paper we show that if one of the matrices of a four-weight spin model is equivalent to the matrix of a Potts model or a cyclic model as type II matrix and , then the spin model is gauge equivalent to a Potts model or a cyclic model up to simultaneous permutations on rows and columns. Using this fact and Nomura's result  we show that every four-weight spin model of size is gauge equivalent to either a Potts model or a cyclic model up to simultaneous permutations on rows and columns.
Keywords: four-weight spin models, Bose-Mesner algebra, gauge equivalent
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