## Bachelor's Theses

#### Title

On lattice path enumeration

2019

#### Document Type

Bachelor's Thesis

#### Degree Name

Bachelor of Science in Mathematics with specialization in Business Applications

Mathematics

#### College

College of Science

#### Department/Unit

Mathematics and Statistics Department

#### 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.

html

English

Electronic

CDTU017648

#### Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

COinS