Solvability of linear equations within weak mixing sets
Combinatorics
2009-11-10 v2 Dynamical Systems
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.
Cite
@article{arxiv.0704.0600,
title = {Solvability of linear equations within weak mixing sets},
author = {Alexander Fish},
journal= {arXiv preprint arXiv:0704.0600},
year = {2009}
}
Comments
30 pages, to appear in Israel Journal of Mathematics