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Solvability of linear equations within weak mixing sets

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Abstract

We introduce a new class of “random“ subsets of natural numbers, WM sets. This class contains normal sets (sets whose characteristic function is a normal binary sequence). We establish necessary and sufficient conditions for solvability of systems of linear equations within every WM set and within every normal set. We also show that any partition-regular system of linear equations with integer coefficients is solvable in any WM set.

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  1. Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Dr., Madison, WI, 53706-1388, USA

    Alexander Fish

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  1. Alexander Fish
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Correspondence to Alexander Fish.

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Fish, A. Solvability of linear equations within weak mixing sets. Isr. J. Math. 184, 477–504 (2011). https://doi.org/10.1007/s11856-011-0077-6

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  • DOI: https://doi.org/10.1007/s11856-011-0077-6

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