Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T05:10:35.080Z Has data issue: false hasContentIssue false
  • English
  • Français

Factorial moments for random mappings by means of indicator variables

Part of: Graph theory

Published online by Cambridge University Press:  14 July 2016

Brian J. English
Brian J. English*
Affiliation:
University of Leicester
*
∗ Postal address: Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, UK.
Get access Rights & Permissions [Opens in a new window]

Abstract

A simple identity for the incomplete factorial of sums of zero-one variables is exploited to provide the factorial moments of the number of components and the number of cyclical elements of the random mapping (T, {pi}) considered by Ross (1981).

Keywords

RANDOM GRAPH

MSC classification

Primary: 05C80: Random graphs
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 1 , March 1993 , pp. 167 - 174
Copyright
Copyright © Applied Probability Trust 1993 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bollabás, B. (1985) Random Graphs. Academic Press, London.Google Scholar
Burtin, Y. D. (1980) On a simple formula for random mappings and its applications. J. Appl. Prob. 17, 403–414.Google Scholar
Donnelly, P. J. and Tavaré, S. (1986) The ages of alleles and coalescent. Adv. Appl. Prob. 18, 1–19.CrossRefGoogle Scholar
Feller, W. (1957) An Introduction to Probability Theory and its Applications, Vol. 1, 2nd edn. Wiley, New York.Google Scholar
Harris, B. (1960) Probability distributions related to random mappings. Ann. Math. Statist. 31, 1045–1062.CrossRefGoogle Scholar
Jaworski, J. (1984) On a random mapping (T, Pi). J. Appl. Prob. 21, 186–191.Google Scholar
Kupka, J. (1990) The distribution and moments of the number of components of a random function. J. Appl. Prob. 27, 202–207.CrossRefGoogle Scholar
Ross, S. M. (1981) A random graph. J. Appl. Prob. 18, 309–315.Google Scholar
Stanley, R. P. (1986) Enumerative Combinatorics, Vol. 1, Wadsworth and Brooks/Cole, Monterey, CA.Google Scholar