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Rado Numbers for the Equation ∑i = 1m − 1 xi + c = xm, for Negative Values of c

✍ Scribed by Wojciech Kosek; Daniel Schaal

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 90 KB
Volume: 27
Category: Article
ISSN: 0196-8858
DOI: 10.1006/aama.2001.0762

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✦ Synopsis

For every integer m ≥ 3 and every integer c, let r m c be the least integer, if it exists, such that for every 2-coloring of the set 1 2 r m c there exists a monochromatic solution to the equation

The values of r m c were previously known for all values of m and all nonnegative values of c. In this paper, exact values of r m c are found for all values of m and all values of c such that -m + 2 < c < 0 or c < -m -1 m -2 . Upper and lower bounds are given for the remaining values of c.

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Rado Numbers for the Equation ∑i&#xa0;=&#xa0;1m&#xa0;−&#xa0;1&#xa0;xi&#xa0;+&#xa0;c&#xa0;=&#xa0;xm, for Negative Values of c

✦ Synopsis

Rado Numbers for the Equation ∑i = 1m − 1 xi + c = xm, for Negative Values of c