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
thuang@math.nctu.edu.tw

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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