Totally Multicolored Rado Numbers For the Equation x_1 + x_2 + x_3 + ... + x_(m−1) = x_m

Author

Skylar Halverson, South Dakota State UniversityFollow

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).

Library of Congress Subject Headings

Ramsey theory.
Combinatorial analysis.
Rado numbers

Number of Pages

32

Publisher

South Dakota State University

Recommended Citation

Halverson, Skylar, "Totally Multicolored Rado Numbers For the Equation x_1 + x_2 + x_3 + ... + x_(m−1) = x_m" (2022). Electronic Theses and Dissertations. 399.
https://openprairie.sdstate.edu/etd2/399