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On Lattice Paths with Several Diagonal Steps

Published online by Cambridge University Press:  20 November 2018

S.G. Mohanty
Affiliation:
Indian Institute of Technology, New Delhi
B.R. Handa
Affiliation:
Indian Institute of Technology, New Delhi
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In this note we consider the enumeration of unrestricted and restricted minimal lattice paths from (0, 0) to (m, n), with the following (μ + 2) moves, μ being a positive integer. Let the line segment between two lattice points on which no other lattice point lies be called a step. A lattice path at any stage can have either (1) a vertical step denoted by S0, or (2) a diagonal step parallel to the line x = ty (t = 1,…, μ), denoted by St, or (3) a horizontal step, denoted by Sμ+1.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Bizley, M.T.J., Derivations of new formula for the number of minimal lattice paths. Jour. Inst, of Actuaries 80 (1954) 55-62.Google Scholar
2. Mohanty, S.G., Some convolutions with multinomial coefficients and related probability distributions. SIAM Review 8 (1966) 501-509.Google Scholar
3. Mohanty, S.G., Restricted compositions Fibonacci Quarterly 5 (1967) 223-234.Google Scholar
4. Moser, L. and Zayachkowaski, W., Lattice paths with diagonal steps. Scripta Mathematica 26 (1961) 223-229.Google Scholar
5. Rohatgi, V.K., A note on lattice paths with diagonal steps. Canad. Math. Bull. 7 (1964) 470-472.Google Scholar