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Counting Near-Perfect Matchings on Cm × Cn Tori of Odd Order in the Maple System

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Abstract

In the Maple computer algebra system, a set of recurrence relations and associated generating functions is derived for the number of near-perfect matchings on \({{C}_{m}} \times {{C}_{n}}\) tori of odd order at fixed values of the parameter m (\(3 \leqslant m \leqslant 11\)). The identity of the recurrence relations for the number of perfect and near-perfect matchings is revealed for the same value of m. An estimate for the number of near-perfect matchings is obtained at large odd m when \(n \to \infty \).

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  1. Petrozavodsk State University, pr. Lenina 33, 185910, Petrozavodsk, Republic of Karelia, Russia

    S. N. Perepechko

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  1. S. N. Perepechko
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Correspondence to S. N. Perepechko.

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Translated by Yu. Kornienko

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Perepechko, S.N. Counting Near-Perfect Matchings on Cm × Cn Tori of Odd Order in the Maple System. Program Comput Soft 45, 65–72 (2019). https://doi.org/10.1134/S0361768819020075

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  • DOI: https://doi.org/10.1134/S0361768819020075

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