Document Type

Thesis - Open Access

Award Date

2022

Degree Name

Master of Science (MS)

Department / School

Mathematics and Statistics

Abstract

A set is called Totally Multicolored (TMC) if no elements in the set are colored the same. For all natural numbers t, m, let R(t, m) be the least natural number n such that for every t-coloring of the set {1, 2, 3, ..., R(t, m)} there exist a solution set {x_1, x_2, . . ., x_m} to L(m), x_1 + x_2 + x_3 + ... + x_(m−1) = x_m such that x_i does not equal x_j for all i that does not equal j, that avoids being Totally Multicolored. This paper shows a function to find R(t,m) for any t greater than or equal to 1 and m greater than or equal to 3. See the abstract in the text for the function that gives R(t,m).

Number of Pages

32

Publisher

South Dakota State University

Included in

Mathematics Commons

Share

COinS
 

Rights Statement

In Copyright