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

Ramsey, L. Thomas; Graham, Colin C.

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

Authors

Description

Let $e^{2πi\Q}$ denote the set of roots of unity. We consider subsets $E\subset e^{2πi\Q}$ that are quasi-independent or algebraically independent (as subsets of the discrete plane). A bijective map on $e^{2πi\Q}$ 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.