On topological spin models and generalized Δ-Y transformations

We extend the exactly triply regular Bose-Mesner algebras and the associated @D-Y transformations introduced by Jaeger [J. Algebraic Combin. 4 (1995) 103-144] to evaluate the partition function of a topological spin model. We also study the inverse problem for dual pairs of Bose-Mesner algebras in relation to topological spin models.

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