Title

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 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.

Abstract Format

html

Language

English

Format

Electronic

Accession Number

CDTU017648

Shelf Location

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

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