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Dimer coverings and Kekulé structures on honeycomb lattice strips

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Abstract

The problem of covering every site of a subsection of the honeycomb lattice with disjoint edges is considered. It is pointed out that a type of long-range order associated to such coverings can occur, so that different phases can arise as a consequence of the subsection's boundaries. These features are quantitatively investigated via a new analytic solution for a class of strips of arbitrary widths, arbitrary lengths, and arbitrary long-range-order values. Relations to work on the dimer covering problem of statistical mechanics and especially to the resonance theory of benzenoid hydrocarbons are noted.

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Authors and Affiliations

  1. Theoretical Chemical-Physics Group, Department of Marine Sciences, Texas A and M University at Galveston, 77553, Galveston, TX, USA

    D. J. Klein, G. E. Hite, W. A. Seitz & T. G. Schmalz

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  1. D. J. Klein
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  2. G. E. Hite
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  3. W. A. Seitz
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  4. T. G. Schmalz
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Supported by The Robert A. Welch Foundation of Houston, Texas

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Klein, D.J., Hite, G.E., Seitz, W.A. et al. Dimer coverings and Kekulé structures on honeycomb lattice strips. Theoret. Chim. Acta 69, 409–423 (1986). https://doi.org/10.1007/BF00526700

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  • DOI: https://doi.org/10.1007/BF00526700

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