Document Type
Thesis - University Access Only
Award Date
2009
Degree Name
Master of Science (MS)
Department / School
Mathematics and Statistics
Abstract
For any t ∈ [special characters omitted], let n = Rs( t) be the least integer n, such that for every t-coloring of the set [1, n], one of the following two cases will occur: (a) There exists a solution (x 1, x2, x3) to the Schur Equation x1 + x 2 = x3, such that Δ(x 1) = Δ(x2) = Δ(x 3). (This is known as a monochromatic solution.) (b) There exists a solution (x1, x2, x3) to the Schur Equation such that Δ(x i) ≠ Δ(xj) for every i, j where 1 ≤ i < j ≤ 3. (This is known as a totally multicolored solution.) The number n = Rs( t) is known as the t-color selectivity Rado Number. The main results section will show that for every t ∈ [special characters omitted], [special characters omitted]Furthermore, if t is even, there exists a unique coloring of maximal length. If t is odd, there exist [special characters omitted] different colorings of maximal length.
Library of Congress Subject Headings
Combinatorial analysis
Ramsey theory
Rado numbers
Format
application/pdf
Number of Pages
47
Publisher
South Dakota State University
Recommended Citation
Bergwell, Mike, "T-color Selectivity Rado numbers" (2009). Electronic Theses and Dissertations. 1561.
https://openprairie.sdstate.edu/etd2/1561
