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A note on the monomer dimer problem

Published online by Cambridge University Press:  24 October 2008

J. A. Bondy  and
D. J. A. Welsh
J. A. Bondy
Affiliation:
Mathematical Institute, Oxford
D. J. A. Welsh
Affiliation:
Mathematical Institute, Oxford
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Extract

In this note we determine a lower bound for the number of different configurations of monomers and dimers on the hypercubical lattice. This combinatorial problem has important applications in statistical mechanics ((1)) and solid state chemistry.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 3 , July 1966 , pp. 503 - 505
Copyright
Copyright © Cambridge Philosophical Society 1966

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References

REFERENCES

(1)Fisher, M. E. and Stephenson, J.Statistical mechanics of dimers on a plane lattice. II. Dimer correlations and monomers. Phys. Rev. 132 (1963), 1411–1431.CrossRefGoogle Scholar
(2)Hammersley, J. M. Existence theorems and Monte Carlo methods for the monomerdimer problem. J. Neyman's Festchrift, pp. 125–146. Wiley and Sons; New York, (1966).Google Scholar
(3)Fisher, M. E.Statistical mechanics of dimers on a plane lattice. Phys. Rev. 124 (1961), 1664–1672.CrossRefGoogle Scholar
(4)Kasteleyn, P. W.The statistics of a dimer lattice. I. Physics, 27 (1961), 1209–1225.Google Scholar