Abstract
The systems of linear equations (homogeneous or inhomogeneous) that are partition regular, over ℕ or ℤ or ℚ, were characterized by Rado. Our aim here is to characterize those systems for which we can guarantee a nonconstant, or injective, solution. It turns out that we thereby recover an equivalence between ℕ and ℤ that is normally lost when one passes from homogeneous to inhomogeneous systems.
This author acknowledges support received from the National Science Foundation (USA) via grant DMS-0243586.
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Hindman, N., Leader, I. (2006). Nonconstant Monochromatic Solutions to Systems of Linear Equations. In: Klazar, M., Kratochvíl, J., Loebl, M., Matoušek, J., Valtr, P., Thomas, R. (eds) Topics in Discrete Mathematics. Algorithms and Combinatorics, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-33700-8_9
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DOI: https://doi.org/10.1007/3-540-33700-8_9
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