Document Type
Thesis - University Access Only
Award Date
2009
Degree Name
Master of Science (MS)
Department / School
Mathematics and Statistics
Abstract
For all integers a and b that satisfy 2 ≤ a ≤ b, let t = rd(S(a), S(b)) be the least integer for S( a) : ax1 + x2 = x3; S(b) : bx1 + x2 = x 3 such that for every coloring Δ : {1, 2, ...t} → {0, 1} there exist integers x1, x 2, and x3 ∈ {1, 2, ...t} such that either ax1 + x 2 = x3 or bx1 + x2 = x3 and Δ( x1) = Δ(x2) = Δ( x3). This t represents the disjunctive Rado number for the set of equations S(a) and S(b). The following theorem is the main result of the paper. Theorem. Let a, b, and r be integers such that 2 ≤ a ≤ b, r is the remainder when (a + 1)2 is divided by b, and 0 ≤ r < b. The disjunctive Rado number for the equations S(a) : ax1 + x2 = x 3 and S(b) : bx1 + x2 = x3 is[special characters omitted]
Library of Congress Subject Headings
Ramsey theory
Combinatorial analysis
Rado numbers
Format
application/pdf
Number of Pages
37
Publisher
South Dakota State University
Recommended Citation
Lane-Harvard, Liz, "Disjunctive Rado numbers for the set of equations ax(,1) + x(,2) = x(,3) and bx(,1) + x(,2) = x(,3)" (2009). Electronic Theses and Dissertations. 1589.
https://openprairie.sdstate.edu/etd2/1589
