An improved upper bound for the 3-Dimensional dimer problem

Duke Mathematical Journal

Volumn 94, Issue 1, 1998, Pages 1-11

  Ciucu, Mihai ^a  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040121962     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-98-09401-7     Document Type: Article

References (14)

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2. d + 2)-vertex model, to appear in J. Algebraic Combin.
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4. J. M. Hammersley, “Existence theorems and Monte Carlo methods for the monomer-dimer problem” in 1966 Research Papers in Statistics (Festschrift J. Neyman), John Wiley, London, 1966,125-146.
5. J. M. Hammersley, An improved lower bound for the multidimensional dimer problem, Proc. Cambridge Philos. Soc. 64 (1968), 455-463.
6. P. W. Kasteleyn, The statistics of dimers on a lattice, I: The number of dimer arrangements on a quadratic lattice, Physica 27 (1961), 1209-1225.
7. H. Minc, An upper bound for the multidimensional dimer problem, Math. Proc. Cambridge Philos. Soc. 83 (1978), 461-462.
8. H. Minc, An asymptotic solution of the multidimensional dimer problem, Linear and Multilinear Algebra 8 (1979/80), 235-239.
9. H. Minc, Review of [12], Math. Reviews, January 1982, article 82a:15004, 63.
10. J. F. Nagle, New series-expansion method for the dimer problem, Phys. Rev. 152 (1966), 190-197.
11. V. B. Priezzhev, The statistics of dimers on a three-dimensional lattice, II: An improved lower bound, J. Statist. Phys. 26 (1981), 829-837.
12. A. Schrijver and W. G. Valiant, On lower bounds for permanents, Nederl. Akad. Wetensch. Indag. Math. 42 (1980), 425-427.
13. R. P. Stanley, Enumerative combinatorics, Vol. I, Wadsworth and Brooks/Cole Math. Ser., Wadsworth and Brooks/Cole, Monterey, Calif., 1986.
14. H. N. V. Temperley and M. E. Fisher, Dimer problem in statistical mechanics—an exact result, Philos. Mag. 6 (1961), 1061-1063.