Solvability of linear equations within weak mixing sets

Details Solvability of linear equations within weak mixing sets Solvability of linear equations within weak mixing sets

2007-04-04

arxiv.org/abs/0704.0600v2

Mathematics

Combinatorics

30 pages, to appear in Israel Journal of Mathematics

Scientific paper

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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