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One-to-one functions on the positive integers

Published online by Cambridge University Press:  14 July 2016

Gedalia Ailam  and
Mahabanoo N. Tata
Gedalia Ailam
Affiliation:
Michigan State University
Mahabanoo N. Tata
Affiliation:
Michigan State University
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Extract

Let {an} be an increasing sequence of positive integers and let be the family of all functions from the positive integers into the positive integers, which satisfy Assume that are random functions with probabilities and for all n > 1 and 0 elsewhere, i.e., all permissible values of f, given the past, are equally likely.

Type
Short Communications
Information
Journal of Applied Probability , Volume 7 , Issue 2 , August 1970 , pp. 505 - 507
Copyright
Copyright © Applied Probability Trust 1970 

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References

[1] Neuts, M. F. (1968) Are many functions on the positive integers one-to-one? Math. Magazine 41, 103–109.CrossRefGoogle Scholar
[2] Rényi, A. (1962) Théorie des éléments saillants d'une suite d'observations. Colloquium on Combinatorial Methods in Probability Theory. Math. Inst., Aarhus Univ., Denmark.Google Scholar
[3] LoéVe, M. (1963) Probability Theory. 3rd ed. Van Nostrand, Princeton.Google Scholar