On lattice path enumeration
Date of Publication
2019
Document Type
Bachelor's Thesis
Degree Name
Bachelor of Science in Mathematics with specialization in Business Applications
Subject Categories
Mathematics
College
College of Science
Department/Unit
Mathematics and Statistics
Abstract/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.
Abstract Format
html
Language
English
Format
Electronic
Accession Number
CDTU017648
Shelf Location
Archives, The Learning Commons, 12F, Henry Sy Sr. Hall
Recommended Citation
Dionisio, C., & Kim, J. (2019). On lattice path enumeration. Retrieved from https://animorepository.dlsu.edu.ph/etd_bachelors/18563
