On the number of benzenoid hydrocarbons |
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Authors: | Vöge Markus Guttmann Anthony J Jensen Iwan |
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Institution: | Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia. |
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Abstract: | We present a new algorithm which allows a radical increase in the computer enumeration of benzenoids b(h) with h hexagons. We obtain b(h) up to h = 35. We prove that b(h) approximately const.kappa(h), prove the rigorous bounds 4.789 < or = kappa < or = 5.905, and estimate that kappa = 5.16193016(8). Finally, we provide strong numerical evidence that the generating function summation operator b(h)z(h) approximately A(z) log(1 - kappa z), estimate A(1/kappa) and predict the subleading asymptotic behavior. We also provide compelling arguments that the mean-square radius of gyration (h) of benzenoids of size h grows as h(2 nu), with nu = 0.64115(5). |
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