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AN ASYMPTOTIC FORMULA FOR exp(x/1-x)

  • Published : 2002.04.01

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.

Keywords

transitive tournament;exponetial generating function;recursive formula;admissible;Hayman's method

References

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