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ON THE DISJUNCTIVE RADO NUMBER OF THE EQUATIONS ax1 = x2 AND bx1 + x2 = x3

Description:

For a given system of linear equations L, the Rado number of the system is the least integer n for which every t-coloring of {1,...,n} contains a monochromatic solution of one of the equations in L, if such an integer exists. In this thesis, the 2-color disjunctive Rado numbers for the equations ax1 = x2 and bx1 + x2 = x3 are determined for more than half of all values of a and b.

Keyword:

Ramsey theory, disjunctive Rado numbers, and Schur numbers

Subject:

Mathematics

Creator:

Purcilly, Adam

Contributor:

Dr. Brian Hopkins, Thesis Advisor

Owner:

lsquillante@saintpeters.edu

Publisher:

Saint Peter's University

Date Uploaded:

10/14/2020

Date Modified:

10/14/2020

Date Created:

Spring 2013

Rights Statement:

In Copyright

Resource Type:

Research Paper