Permutation and extension for planar quasiindependent subsets of the roots of unity
Abstract
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 quasiindependent 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 quasiindependent sets, and those maps are characterized. The effect on the size of quasiindependent sets in the $n^{th}$ roots of unity $Z_n$ of increasing a prime factor of $n$ is studied.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606546
 Bibcode:
 2006math......6546R
 Keywords:

 Mathematics  Functional Analysis;
 Primary: 42A16;
 43A46;
 Secondary 11A25;
 11B99;
 11lxx