Date of Award

Fall 12-2016

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Timothy B. Flowers, Ph.D.

Second Advisor

Rachelle R. Bouchat, Ph.D.

Third Advisor

Kimberly J. Burch, Ph.D.

Abstract

In this thesis we will review the beginnings of integer partitions. We will further explore past research done on restricted partition functions, specifically those of the m-ary and hyper-m-ary partitions for m ≥ 2. The main content of this paper explores the kth m–ary partition function. For m, k ≥ 2, let the kth m–ary partition function, bm(k, n), be the number of ways we can write a positive integer n as a sum of powers of m using at most k of each power. In this thesis we will classify the monotonicity properties of bm(k, n) by considering the congruence classes of n and k modulo m, and define a relationship between bm(1, n) and writing n in base m.

Included in

Mathematics Commons

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