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arXiv · 0704.0600

Solvability of linear equations within weak mixing sets

Alexander Fish
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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 partition-regular system of linear equations with integer coefficients is solvable in any WM set.

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Alexander Fish. 2009-11-10. Solvability of linear equations within weak mixing sets. https://arxiv.org/abs/0704.0600

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