Exact value of 3 color weak Rado number
For integers k, n, c with k, n ≥ 1 and c ≥ 0, the n color weak Rado number W Rk(n, c) is defined as the least integer N, if it exists, such that for every n coloring of the set {1, 2, ..., N}, there exists a monochromatic solution in that set to the equation x1 + x2 + ... + xk + c = xk+1, such that...
| Autores: | , , , |
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| Formato: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2016 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/136592 |
| Acesso em linha: | https://hdl.handle.net/11441/136592 https://doi.org/10.1016/j.endm.2016.09.042 |
| Access Level: | acceso abierto |
| Palavra-chave: | Schur numbers Sum-free sets Weak Schur numbers Rado numbers Weak Rado numbers |
| Resumo: | For integers k, n, c with k, n ≥ 1 and c ≥ 0, the n color weak Rado number W Rk(n, c) is defined as the least integer N, if it exists, such that for every n coloring of the set {1, 2, ..., N}, there exists a monochromatic solution in that set to the equation x1 + x2 + ... + xk + c = xk+1, such that xi = xj when i = j. If no such N exists, then W Rk(n, c) is defined as infinite. In this work, we consider the main issue regarding the 3 color weak Rado number for the equation x1 + x2 + c = x3 and the exact value of the W R2(3, c) = 13c + 22 is established. |
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