On random mapping patterns

Abstract

Random mapping patterns may be represented by unlabelled directed graphs in which each point has out-degree one. We determine the asymptotic behaviour of various parameters associated with such graphs, such as the expected number of points belonging to cycles and the expected number of components.

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Dedicated to Paul Erdős on his seventieth birthday

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Meir, A., Moon, J.W. On random mapping patterns. Combinatorica 4, 61–70 (1984). https://doi.org/10.1007/BF02579158

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AMS subject classification (1980)

  • 05 C 30
  • 05 C 20