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Explicit Expressions for a Class of Permutation Problems

Published online by Cambridge University Press:  20 November 2018

Morton Abramson
Morton Abramson*
Affiliation:
McGill University
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Extract

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The purpose of this paper is to give some explicit formulae for probability problems such as those dealing with maximum runs upon tossing a coin n times in succession. Although the actual computation involved is quite lengthy, and generating functions can be used for approximations, the lemmas obtained may be of some interest in themselves.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 3 , September 1964 , pp. 345 - 350
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Feller, W., An Introduction to Probability Theory and Its Applications, Vol. 2, 2nd Edition, John Wiley, N. Y., Chapt. XI, p.260.Google Scholar
2. Kaplansky, I., Solution of the "Problème"des Ménages", Bull. Amer. Math. Soc., Vol. 49 (1943), pp. 784–785.Google Scholar
3. Mendelsohn, N. S., The Asymptotic Series for a Certain Class of Permutation Problems, Canadian Journal of Math., Vol. 8(1956), p. 238.Google Scholar