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Perfect matchings on a type of lattices with toroidal boundary

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Abstract

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.

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Authors and Affiliations

  1. Faculty of Science, Jiangxi University of Science and Technology, Ganzhou, 341000, China

    Xing Feng

  2. School of Mathematical Science, Xiamen University, Xiamen, 361005, China

    Lian-zhu Zhang

  3. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, China

    Ming-zu Zhang

Authors
  1. Xing Feng
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  2. Lian-zhu Zhang
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  3. Ming-zu Zhang
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Corresponding author

Correspondence to Xing Feng.

Additional information

Supported by the National Natural Science Foundation of China (Grant No. 11471273; 11671186).

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Feng, X., Zhang, Lz. & Zhang, Mz. Perfect matchings on a type of lattices with toroidal boundary. Appl. Math. J. Chin. Univ. 34, 33–44 (2019). https://doi.org/10.1007/s11766-019-3502-y

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  • DOI: https://doi.org/10.1007/s11766-019-3502-y

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