arXiv 0704.06002007-04math.COmath.DS

Solvability of linear equations within weak mixing sets

Alexander Fish

备注：: 30 pages, to appear in Israel Journal of Mathematics

英文摘要：

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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