Perfect matchings on a type of lattices with toroidal boundary

Enumeration of perfect matchings on graphs has a longstanding interest in combinatorial mathematics. In this paper, we obtain some explicit expressions of the number of perfect matchings for a type of Archimedean lattices with toroidal boundary by applying Tesler's crossing orientations to obta...

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Bibliographic Details
Published inApplied Mathematics-A Journal of Chinese Universities Vol. 34; no. 1; pp. 33 - 44
Main Authors Feng, Xing, Zhang, Lian-zhu, Zhang, Ming-zu
Format Journal Article
LanguageEnglish
Published Hangzhou Editorial Committee of Applied Mathematics - A Journal of Chinese Universities 01.03.2019
Springer Nature B.V
Subjects
Applications of Mathematics
Combinatorial analysis
Enumeration
Lattices (mathematics)
Mathematics
Mathematics and Statistics
perfect matching
toroidal boundary
05C70
Archimedean lattice
Pfaffan orientation
05C30
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Summary:Enumeration of perfect matchings on graphs has a longstanding interest in combinatorial mathematics. In this paper, we obtain some explicit expressions of the number of perfect matchings for a type of Archimedean lattices with toroidal boundary by applying Tesler's crossing orientations to obtain some Pfaffian orientations and enumerating their Pfaffians.
ISSN:1005-1031
1993-0445
DOI:10.1007/s11766-019-3502-y