Theoretica chimica acta

, Volume 69, Issue 5–6, pp 409–423 | Cite as

Dimer coverings and Kekulé structures on honeycomb lattice strips

  • D. J. Klein
  • G. E. Hite
  • W. A. Seitz
  • T. G. Schmalz
Article

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.

Key words

Kekulé structure enumeration Dimer covering enumeration 1-Factor enumeration Benzenoid π-network polymers Long-range order Bond localization Edge reactivity Graph theory Transfer matrices 

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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • D. J. Klein
    • 1
  • G. E. Hite
    • 1
  • W. A. Seitz
    • 1
  • T. G. Schmalz
    • 1
  1. 1.Theoretical Chemical-Physics Group, Department of Marine SciencesTexas A and M University at GalvestonGalvestonUSA

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