Artículo
Exact values and lower bounds on the n-color weak Schur numbers for n = 2, 3
Autor/es | Ahmed, T.
Boza Prieto, Luis Revuelta Marchena, María Pastora Sanz Domínguez, María Isabel |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2023-08-23 |
Fecha de depósito | 2023-09-27 |
Publicado en |
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Resumen | For integers k, n with k, n ≥ 1, the n-color weak Schur number WSk (n) is defined as
the least integer N, such that for every n-coloring of the integer interval [1, N], there
exists a monochromatic solution x1,..., xk , ... For integers k, n with k, n ≥ 1, the n-color weak Schur number WSk (n) is defined as the least integer N, such that for every n-coloring of the integer interval [1, N], there exists a monochromatic solution x1,..., xk , xk+1 in that interval to the equation: x1 + x2 +···+ xk = xk+1, with xi = x j , when i = j. In this paper, we obtain the exact values of W S6(2) = 166, W S7(2) = 253, W S3(3) = 94 and W S4(3) = 259 and we show new lower bounds on n-color weak Schur number WSk (n) for n = 2, 3. |
Cita | Ahmed, T., Boza Prieto, L., Revuelta Marchena, M.P. y Sanz Domínguez, M.I. (2023). Exact values and lower bounds on the n-color weak Schur numbers for n = 2, 3. The Ramanujan Journal, 62, 347-363. https://doi.org/10.1007/s11139-023-00760-y. |
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