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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