Permutation and extension for planar quasi-independent subsets of the roots of unity

Details Permutation and extension for planar quasi-independent subsets of the roots of unity Permutation and extension for planar quasi-independent subsets of the roots of unity

2006-06-21

arxiv.org/abs/math/0606546v1

Mathematics

Functional Analysis

Scientific paper

Let $e^{2\pi i\Q}$ denote the set of roots of unity. We consider subsets $E\subset e^{2\pi i\Q}$ that are quasi-independent or algebraically independent (as subsets of the discrete plane). A bijective map on $e^{2\pi i\Q}$ preserves the algebraically independent sets iff it preserves the quasi-independent sets, and those maps are characterized. The effect on the size of quasi-independent sets in the $n^{th}$ roots of unity $Z_n$ of increasing a prime factor of $n$ is studied.

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