Spinors, lattices, and classification of integral Apollonian disk packings
Metric Geometry
2020-01-17 v1
Abstract
A parametrization of integral Descartes configurations (and effectively Apollonian disk packings) by pairs of two-dimensional integral vectors is presented. The vectors, called here tangency spinors defined for pairs of tangent disks, are spinors associated to the Clifford algebra for three-dimensional Minkowski space. A version with Pauli spinors is given. The construction provides a novel interpretation to the known Diophantine equation parametrizing integral Apollonian packings.
Keywords
Cite
@article{arxiv.2001.05866,
title = {Spinors, lattices, and classification of integral Apollonian disk packings},
author = {Jerzy Kocik},
journal= {arXiv preprint arXiv:2001.05866},
year = {2020}
}
Comments
35 pages, 20 figures