On lattice path enumeration
A lattice path from (a b) to (c d) on the grid Z Z with step set S is a nite sequence of ordered pairs (x0 y0) (x1 y1) : : : (xn yn) on Z Z such that the initial point satisfies (a b) = (x0 y0), the terminal point satisfies (c d) = (xn yn), and the points in between satisfy (xi+1 yi+1) = (xi yi)+ fo...
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| Main Authors: | , |
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| Format: | text |
| Language: | English |
| Published: |
Animo Repository
2019
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| Subjects: | |
| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/18563 |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | A lattice path from (a b) to (c d) on the grid Z Z with step set S is a nite sequence of ordered pairs (x0 y0) (x1 y1) : : : (xn yn) on Z Z such that the initial point satisfies (a b) = (x0 y0), the terminal point satisfies (c d) = (xn yn), and the points in between satisfy (xi+1 yi+1) = (xi yi)+ for some 2 S where we assume that a c and b d. In this paper, we focus on lattice paths from (a b) to (c d) on the grid Z Z with step sets S = f(0 1) (1 0)g and S = f(1 0) (0 1) (1 1)g. We discuss various formulas in counting two-step and three-step lattice paths with various restrictions. This thesis is an exposition of the work of Christian Krattenthaler (2015) on lattice path enumeration. |
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