Location of Repository

We show that for any two linear homogeneous equations E0, E1, each with at least three variables and coefficients not all the same sign, any 2-coloring of Z + admits monochromatic solutions of color 0 to E0 or monochromatic solutions of color 1 to E1. We define the 2-color off-diagonal Rado number RR(E0, E1) to be the smallest N such that [1, N] must admit such solutions. We determine a lower bound for RR(E0, E1) in certain cases when each Ei is of the form a1x1 +... + anxn = z as well as find the exact value of RR(E0, E1) when each is of the form x1 + a2x2 +... + anxn = z. We then present a Maple package that determines upper bounds for off-diagonal Rado numbers of a few particular types, and use it to quickly prove two previous results for diagonal Rado numbers.

Year: 2010

OAI identifier:
oai:CiteSeerX.psu:10.1.1.178.5348

Provided by:
CiteSeerX

Download PDF:To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.