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Derivation of a New Formula for the Number of Minimal Lattice Paths From (0,0) to (km,kn) Having Just t Contacts with the Line my=nx and Having No Points Above This Line; and a Proof of Grossman's Formula for the Number of Paths Which May Touch But Do Not Rise Above This Line

Published online by Cambridge University Press:  18 August 2016

M. T. L. Bizley
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Journal of the Institute of Actuaries , Volume 80 , Issue 1 , June 1954 , pp. 55 - 62
Copyright
Copyright © Institute and Faculty of Actuaries 1954

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References

(1) Whitworth, W. A. (1901). Choice and Chance, 5th ed. Cambridge.Google Scholar
(2) Dvoretzky, A. and Motzkin, Th. (1947). A problem of arrangements. Duke Math. J. 14, no. 2.Google Scholar
(3) Grossman, Howard D. (1950). Another extension of the ballot problem. Scr. Math., N. Y., 16, 120.Google Scholar
(4) Grossman, Howard D. (1950). Paths in a lattice triangle. Scr. Math., N.Y., 16, 207.Google Scholar