Abstract
The number of perfect rnatchings for the linear 2 × 2 ×n cubic lattice was analytically derived by diagonalizing the skew—symmetric 4n × 4n determinant, whose non—zero off—diagonal elements are either ±1 or ±i (pure imaginary number). The basic formulation invoking the matrix manipulation follows that of Kasteleyn, but the result obtained in this paper is the first example of the analytical solution for a special case of the three-dimensional Ising model.
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received by the Publisher 20 September 1989
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Narumi, H., Hosoya, H. Proof of the generalized expressions for the number of perfect matchings of polycube graphs. J Math Chem 3, 383–391 (1989). https://doi.org/10.1007/BF01169019
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DOI: https://doi.org/10.1007/BF01169019