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On a random mapping (T, Pj)

Published online by Cambridge University Press:  14 July 2016

Jerzy Jaworski
Jerzy Jaworski*
Affiliation:
Adam Mickiewicz University, Poznań
*
∗ Postal address: Institute of Mathematics, Adam Mickiewicz University, Matejki 48/49, 60–769 Poznań, Poland.
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Abstract

A random mapping (T,Pj) of a finite set V into itself is studied. We give a new proof of the fundamental lemma of [6]. Our method leads to the derivation of several results which cannot be deduced from [6]. In particular we determine the distribution of the number of components, cyclical points and ancestors of a given point.

Keywords

RANDOM GRAPH
Type
Short Communications
Information
Journal of Applied Probability , Volume 21 , Issue 1 , March 1984 , pp. 186 - 191
Copyright
Copyright © Applied Probability Trust 1984 

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References

[1] Burtin, Y. D. (1980) On a simple formula for random mappings and its applications. J. Appl. Prob. 17, 403–414.CrossRefGoogle Scholar
[2] Harris, B. (1960) Probability distribution related to random mappings. Ann. Math. Statist. 31, 1045–1062.Google Scholar
[3] Jaworski, J. (1983) On the connectedness of a random bipartite mapping. In Proc. Graph Theory Conf. Lagów, 1981. Lecture Notes in Mathematics 1018, Springer-Verlag, Berlin, 69–14.Google Scholar
[4] Jaworski, J. (1983) On some model of a random mapping. In Graphs and Other Combinatorial Topics. Teubner Publishing House, Leipzig.Google Scholar
[5] Katz, L. (1955) Probability of indecomposability of a random mapping function. Ann. Math. Statist. 26, 512–517.Google Scholar
[6] Ross, S. M. (1981) A random graph. J. Appl. Prob. 16, 309–316.Google Scholar
[7] Sachkov, V. N. (1977) Combinatorial Methods in Discrete Mathematics (in Russian). Nauka, Moscow.Google Scholar
[8] Sachkov, V. N. (1978) Probabilistic Methods in Combinatorial Analysis (in Russian). Nauka, Moscow.Google Scholar
[9] Stepanov, V. E. (1969) Limit distributions of certain characteristics of random mappings. Theory Prob. Appl. 14, 612–626.CrossRefGoogle Scholar
[10] Stepanov, V. E. (1971) Random mappings with a single attracting centre. Theory Prob. Appl. 16, 155–161.CrossRefGoogle Scholar