Iwan Jensen J. Stat. Mech. (2009) P02065 doi:10.1088/1742-5468/2009/02/P02065
Iwan Jensen
Show affiliationsWe present an improved parallel algorithm for the enumeration of fixed benzenoids Bh containing h hexagonal cells. We can thus extend the enumeration of Bh from the previous best h = 35 up to h = 50. Analysis of the associated generating function confirms to a very high degree of certainty that Bh~Aκh/h and we estimate that the growth constant κ = 5.161 930 154(8) and the amplitude A = 0.280 8499(1).
E-print Number: 0808.0963
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02.10.Ox Combinatorics; graph theory
31.10.+z Theory of electronic structure, electronic transitions, and chemical binding
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
02.60.-x Numerical approximation and analysis
31.15.-p Calculations and mathematical techniques in atomic and molecular physics
82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
05A15 Exact enumeration problems, generating functions (See also 33Cxx, 33Dxx)
Issue 02 (February 2009)
Received 19 September 2008, accepted for publication 21 January 2009
Published 27 February 2009
Iwan Jensen J. Stat. Mech. (2009) P02065
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