Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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AN ASYMPTOTIC FORMULA FOR exp(x/1-x)

  • Published : 2002.04.01
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Abstract

We show that G(x) = $e^{(x}$(1-x))/ -1 is the exponential generating function for the labeled digraphs whose weak components are transitive tournaments and derive both a recursive formula and an explicit formula for the number of them on n vertices. Moreover, we investigate the asymptotic behavior for the coefficients of G(x) using Hayman's method.d.

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References

  1. Graphical Enumeration F.Harary;E.M.Palmer
  2. J.fur die reine und angewandte Mathematik v.196 A Generalisation of Stirling's Formula W.K.Hayman
  3. Topics on Tournaments J.W.Moon
  4. Generatingfunctionology H.S.Wilf