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Dimers on the kagome lattice I: Finite lattices

Author

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  • Wu, F.Y.
  • Wang, Fa

Abstract

We report exact results on the enumeration of close-packed dimers on a finite kagome lattice with general asymmetric dimer weights under periodic and cylindrical boundary conditions. For symmetric dimer weights, the resulting dimer generating functions reduce to very simple expressions, and we show how the simple expressions can be obtained from the consideration of a spin-variable mapping.

Suggested Citation

  • Wu, F.Y. & Wang, Fa, 2008. "Dimers on the kagome lattice I: Finite lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(16), pages 4148-4156.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:16:p:4148-4156
    DOI: 10.1016/j.physa.2008.02.054
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    Citations

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    Cited by:

    1. Yan, Weigen & Yeh, Yeong-Nan & Zhang, Fuji, 2008. "Dimer problem on the cylinder and torus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6069-6078.
    2. Wang, Fa & Wu, F.Y., 2008. "Dimers on the kagome lattice II: Correlations and the Grassmannian approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(16), pages 4157-4162.
    3. Li, Shuli & Yan, Weigen, 2016. "Dimers on the 33.42 lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 251-257.
    4. Li, Shuli & Yan, Weigen, 2018. "Spanning trees and dimer problem on the Cairo pentagonal lattice," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 34-40.

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