Counting Near-Perfect Matchings on Cm × Cn Tori of Odd Order in the Maple System
- Authors: Perepechko S.N.1
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Affiliations:
- Petrozavodsk State University
- Issue: Vol 45, No 2 (2019)
- Pages: 65-72
- Section: Article
- URL: https://journals.rcsi.science/0361-7688/article/view/176764
- DOI: https://doi.org/10.1134/S0361768819020075
- ID: 176764
Cite item
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 \(n \to \infty \).
About the authors
S. N. Perepechko
Petrozavodsk State University
Author for correspondence.
Email: persn@newmail.ru
Russian Federation,
pr. Lenina 33, Petrozavodsk, Republic of Karelia, 185910