Award Date

May 2018

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Committee Member

Peter Shiue

Second Committee Member

Derrick DuBose

Third Committee Member

Arthur Baragar

Fourth Committee Member

Yi-Tung Chen

Number of Pages

112

Abstract

In this Masters thesis, we examine linear divisible sequences. A linear divisible sequence is any sequence {an}n≥0 that can be expressed by a linear homogeneous recursion relation that is also a divisible sequence. A sequence {an}n≥0 is called a divisible sequence if it has the property that if n|m, then an|am. A sequence of numbers {an}n≥0 is called a linear homogeneous recurrence sequence of order m if it can be written in the form

an+m = p1an+m−1 + p2an+m−2 + · · · + pm−1an+1 + pman, n ≥ 0,

for some constants p1, p2, ..., pm with pm = 0 and initial conditions a0, a1, ..., am−1. We focus on taking products, powers, and products of powers of second order linear divisible sequences in order to construct higher order linear divisible sequences. We hope to find a pattern in these constructions so that we can easily form higher order linear divisible sequence.

Disciplines

Mathematics

Language

English


Included in

Mathematics Commons

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