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An improved upper bound for the $3$-dimensional dimer problem
Mihai Ciucu
Source: Duke Math. J. Volume 94, Number 1
(1998), 1-11.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077230074
Mathematical Reviews number (MathSciNet): MR1635888
Zentralblatt MATH identifier: 0939.05024
Digital Object Identifier: doi:10.1215/S0012-7094-98-09401-7
References
[1] J. A. Bondy and D. J. A. Welsh, A note on the monomer dimer problem, Proc. Cambridge Philos. Soc. 62 (1966), 503–505.
Mathematical Reviews (MathSciNet): MR34:3958
Digital Object Identifier: doi:10.1017/S0305004100040123
[2] M. Ciucu, Higher dimensional Aztec diamonds and a $(2^d+2)$-vertex model, to appear in J. Algebraic Combin.
[3] R. H. Fowler and G. S. Rushbrooke, An attempt to extend the statistical theory of perfect solutions, Trans. Faraday Soc. 33 (1937), 1272–1294.
[4] J. M. Hammersley, Existence theorems and Monte Carlo methods for the monomer-dimer problem, Research Papers in Statistics (Festschrift J. Neyman), John Wiley, London, 1966, pp. 125–146.
Mathematical Reviews (MathSciNet): MR35:2595
Zentralblatt MATH: 0161.15401
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Digital Object Identifier: doi:10.1017/S030500410004305X
[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.
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Digital Object Identifier: doi:10.1017/S0305004100054748
[8] H. Minc, An asymptotic solution of the multidimensional dimer problem, Linear and Multilinear Algebra 8 (1979/80), no. 3, 235–239.
Mathematical Reviews (MathSciNet): MR81e:82063
Zentralblatt MATH: 0431.15006
Digital Object Identifier: doi:10.1080/03081088008817323
[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), no. 4, 829–837.
Mathematical Reviews (MathSciNet): MR84h:82059b
Digital Object Identifier: doi:10.1007/BF01010944
[12] A. Schrijver and W. G. Valiant, On lower bounds for permanents, Nederl. Akad. Wetensch. Indag. Math. 42 (1980), no. 4, 425–427.
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[13] R. P. Stanley, Enumerative combinatorics. Vol. I, The Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, CA, 1986.
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[14] H. N. V. Temperley and Michael E. Fisher, Dimer problem in statistical mechanics—an exact result, Philos. Mag. (8) 6 (1961), 1061–1063.
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