Annals of Combinatorics 4 (2000) 401-412
Some Remarks on Four-Weight Spin Models
Tayuan Huang and Haitao Guo
Department of Applied Mathematics, National Chiao Tung University,
Hsinchu 30050, Taiwan
Graduate School of Mathematics, Kyushu University, Fukuoka 812, Japan
Received March 20, 1998
AMS Subject Classification: 05E30
Abstract. As a generalization of symmetric spin models, a four-weight spin model (X ; W1, W2 , W3 , W4) consists of a finite set X and four non-zero complex matrices indexed by elements of X satisfying certain conditions set for polynomial invariants of links and knots in R3 through their partition functions. We show that W4tW4= tW4W4, lie in a certain symmetric Bose-Mesner algebra using spectral techniques. Based on this algebra, we then show that entries of W1 were essentially determined by its subconstituent algebra.
Keywords: four-weight spin models, Bose-Mesner Algebra, association schemes
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