Discrete Applied Mathematics· 2026Q2
Off-diagonal Rado number for x+y+c=z and x+qy=z
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- Q2SCImago
- 2026year
Short summary
Researchers determined the exact two-color off-diagonal Rado number for a system of linear equations: x+y+c=z and x+qy=z.
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Key points
- The study focuses on off-diagonal Rado numbers for two-colorings of integers.
- The specific linear equations analyzed are x+y+c=z and x+qy=z.
- The exact two-color off-diagonal Rado number, R2(c, q), for this system has been determined.
AI-generated from the title and abstract; the full text is not read.
Abstract
Ramsey-type problems for linear equations began with Schur’s theorem and were systematically generalized by Richard Rado. In the off-diagonal framework for two colors, one considers two different linear equations ( E 1 , E 2 ) and determines the minimum integer N for which any red–blue coloring of { 1,2 , … , N } forces either a red solution of the equation E 1 or a blue solution of the equation E 2 . In this work, we study the off-diagonal Rado numbers for a combination of homogeneous and non-homogeneous linear equations of the forms x + y + c = z and x + q y = z . We determine the exact two-color off-diagonal Rado number, denoted as R 2 ( c , q ) , associated with this system of equations.
The authors' abstract, as published at the source. Discrete Applied Mathematics, 2026 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics