Proof of the generalized expressions for the number of perfect matchings of polycube graphs |
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| Authors: | Hideyuki Narumi Haruo Hosoya |
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| Affiliation: | (1) Department of Chemistry, Hokkaiko University, Sapporo 060, Japan;(2) Department of Chemistry, Ochanomizu University, Bunkyo-ku, Tokyo 112, Japan |
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| 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.received by the Publisher 20 September 1989 |
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