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Some Properties of Compositions and their Application to the Ballot Problem

Published online by Cambridge University Press:  20 November 2018

S. G. Mohanty
S. G. Mohanty*
Affiliation:
State University of New York at Buffalo and McMaster University
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This paper is a continuation of two papers [4], [5] and brings out the solution of the ballot problem in its general form.

In [5], Narayana has considered a generalised occupancy problem which can be viewed as a problem in compositions of integers. In what follows, we use the definitions of [6].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 3 , April 1965 , pp. 359 - 372
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Dvoretzky, A. and Motzkin, Th., A Problem of Arrangements, Duke Mathematical Journal, XIV, (1947), p. 305.Google Scholar
2. Feller, W., An Introduction to Probability Theory and Its Applications, Second Edition, New York, John Wiley and Sons, Inc., 1957.Google Scholar
3. Grossman, H. D., Fun with Lattice Points, Scripta Mathematica, (1946), p. 224.Google Scholar
4. Mohanty, S. G. and Narayana, T. V., Some Properties of Compositions and their Applications to Probability and Statistics I, Biometrische Zeitschrift, Band 3, Heft 4, (1961), p. 252.CrossRefGoogle Scholar
5. Narayana, T. V., A combinatorial problem and its application to probability theory I, Journal of the Indian Society of Agricultural Statistics VII, (1955), p. 169.Google Scholar
6. Narayana, T.V. and Fulton, G. E., A Note on the Compositions of an Integer, Canadian Mathematical Bulletin, Vol. I, (1958), p. 169.CrossRefGoogle Scholar
7. Takács, L., A Generalisation of the Ballot Problem and Its Application in the Theory of Queues, Journal of American Statistical Association, Vol. 57, (1962), p. 327.Google Scholar
8. Takács, L., Ballot Problems, Z. Wahrscheinlichkeitstheorie, Vol. 1, (1962), p. 154.CrossRefGoogle Scholar
9. Gould, H. W., Some Generalisations of Vandermonde' s Convolution, American Mathematical Monthly, Vol. 63, (1956), p. 84.CrossRefGoogle Scholar