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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oai:animorepository.dlsu.edu.ph:etd_bachelors-190762022-02-11T05:30:01Z On lattice path enumeration Dionisio, Celine Kim, Junhee 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. 2019-01-01T08:00:00Z text https://animorepository.dlsu.edu.ph/etd_bachelors/18563 Bachelor's Theses English Animo Repository Mathematics |
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Mathematics Dionisio, Celine Kim, Junhee On lattice path enumeration |
| description |
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. |
| format |
text |
| author |
Dionisio, Celine Kim, Junhee |
| author_facet |
Dionisio, Celine Kim, Junhee |
| author_sort |
Dionisio, Celine |
| title |
On lattice path enumeration |
| title_short |
On lattice path enumeration |
| title_full |
On lattice path enumeration |
| title_fullStr |
On lattice path enumeration |
| title_full_unstemmed |
On lattice path enumeration |
| title_sort |
on lattice path enumeration |
| publisher |
Animo Repository |
| publishDate |
2019 |
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https://animorepository.dlsu.edu.ph/etd_bachelors/18563 |
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1772835099414364160 |