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An upper bound for the multidimensional dimer problem

Published online by Cambridge University Press:  24 October 2008

Henryk Minc
Affiliation:
University of California, Santa Barbara

Abstract

A recently proved upper bound for the permanents of (0,1) matrices is used to improve the Fowler-Rushbrooke upper bound for the constant λd occurring in the d-dimensional dimer problem, d ≥ 3.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

REFERENCES

(1)Brégman, L. M.Certain properties of nonnegative matrices and their permanents. Dokl. Akad. Nauk SSSR 211 (1973), 2730 (Soviet Math. Dokl. 14 (1973), 945949).Google Scholar
(2)Fowler, R. H. and Rushbrooke, G. S.Statistical theory of perfect solutions. Trans. Faraday Soc. 33 (1937), 12721294.CrossRefGoogle Scholar
(3)Hammersley, J. M.Existence theorems and Monte Carlo methods for the monomer-dimer problem. Research papers in statistics: Festschrift for J. Neyman (1966), 125146.Google Scholar
(4)Hammersley, J. M.An improved lower bound for the multidimensional dimer problem. Proc. Cambridge Philos. Soc. 64 (1968), 455463.CrossRefGoogle Scholar
(5)Minc, H.Upper bounds for permanents of (0, 1)-matrices. Bull. Amer. Math. Soc. 69 (1963), 789791.CrossRefGoogle Scholar