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Kekulé structure counts: General formulations for primitive coronoid hydrocarbons

Zählung von Kekulé-Strukturen

  • Anorganische Und Physikalische Chemie
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Summary

The Kekulé structure counts (K) for primitive coronoids are treated. TheK formula which involves the trace of a matrix product is recalled and supplemented with new findings. In this way a kind of symmetry in the mathematical formulations is restored. Another general formulation for theK number is provided in terms of polynomials which, for a somewhat mysterious reason, are identified as the matching polynomials of cycles.

Zusammenfassung

Es werden Kekulé-Strukturzählungen (K) für einfache Coronoide behandelt. Die Formel fürK wird durch neugefundene Eigenschaften ergänzt. So wird eine Art von Symmetrie in den mathematischen Formulierungen erreicht. Eine andere generelle Formulierung derK-Zahlen wird in Form von Polynomen bereitgestellt, welche aus uneinsichtigen Gründen als die passenden Polynome von Cyclen identifiziert wurden.

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Authors and Affiliations

  1. Division of Physical Chemistry, The University of Trondheim, N-7034, Trondheim-NTH, Norway

    Sven J. Cyvin, Bjørg N. Cyvin & Jon Brunvoll

  2. Department of Chemistry, Ochanomizu University, Bunkyo-ku, 112, Tokyo, Japan

    Haruo Hosoya

  3. Department of Mathematics, Xinjiang University, Urumchi, Xinjiang, People's Republic of China

    Fuji Zhang

  4. Department of Marine Sciences, Texas A & M University, TX-77553, Galveston, USA

    Douglas J. Klein

  5. Department of Planning and Statistics, Fuzhou University, Fuzhou, Fujian, People's Republic of China

    Rongsi Chen

  6. Max-Planck-Institut für Strahlenchemie, D-W-4330, Mühlheim a. d. Ruhr, Federal Republic of Germany

    Oskar E. Polansky

Authors
  1. Sven J. Cyvin
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  2. Bjørg N. Cyvin
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  3. Jon Brunvoll
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  4. Haruo Hosoya
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  5. Fuji Zhang
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  6. Douglas J. Klein
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  7. Rongsi Chen
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  8. Oskar E. Polansky
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Cyvin, S.J., Cyvin, B.N., Brunvoll, J. et al. Kekulé structure counts: General formulations for primitive coronoid hydrocarbons. Monatsh Chem 122, 435–444 (1991). https://doi.org/10.1007/BF00809795

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  • DOI: https://doi.org/10.1007/BF00809795

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