q-Series Arising From The Study of Random Graphs

  • Authors:

  • George E. Andrews;Davide Crippa;Klaus Simon

  • Affiliations:

  • -;-;-

  • Venue:
  • SIAM Journal on Discrete Mathematics
  • Year:
  • 1997

  • Counting by coin tossings

    ASIAN'04 Proceedings of the 9th Asian Computing Science conference on Advances in Computer Science: dedicated to Jean-Louis Lassez on the Occasion of His 5th Cycle Birthday

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Abstract

This paper deals with q-series arising from the study of the transitive closure problem in random acyclic digraphs. In particular, it presents an identity involving divisor generating functions which allows us to determine the asymptotic behavior of polynomials defined by a general class of recursive equations, including the polynomials for the mean and the variance of the size of the transitive closure in random acyclic digraphs.