The localglobal principle for integral bends in orthoplicial Apollonian sphere packings
Abstract
We introduce an orthoplicial Apollonian sphere packing, which is a sphere packing obtained by successively inverting a configuration of 8 spheres with 4orthplicial tangency graph. We will show that there are such packings in which the bends of all constituent spheres are integral, and establish the asymptotic localglobal principle for the set of bends in these packings.
 Publication:

arXiv eprints
 Pub Date:
 January 2014
 arXiv:
 arXiv:1401.2980
 Bibcode:
 2014arXiv1401.2980N
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Group Theory;
 Mathematics  Metric Geometry;
 11D85;
 52C17;
 20H05;
 11F06;
 11E39
 EPrint:
 36 pages, 11 figures