Spinors, lattices, and classification of integral Apollonian disk\n packings

2020/01/15 by Jerzy Kocik, Kocik, Jerzy · 2 citations
Mathematics · Medicine · #Algebraic and Geometric Analysis #Medical and Biological Sciences

paper · pdf · doi:10.48550/arxiv.2001.05866

Abstract

A parametrization of integral Descartes configurations (and effectively\nApollonian disk packings) by pairs of two-dimensional integral vectors is\npresented. The vectors, called here tangency spinors defined for pairs of\ntangent disks, are spinors associated to the Clifford algebra for\nthree-dimensional Minkowski space. A version with Pauli spinors is given. The\nconstruction provides a novel interpretation to the known Diophantine equation\nparametrizing integral Apollonian packings.\n

Citations

• Spinors and Descartes configurations of disks
• Apollonian coronas and a new Zeta function

Cited by

• Integral spinors, Apollonian disk packings, and Descartes groups
• Apollonian depth, spinors, and the super-Dedekind tessellation

Related

• Integral spinors, Apollonian disk packings, and Descartes groups
• Spinors and Descartes configurations of disks
• Apollonian depth, spinors, and the super-Dedekind tessellation
• Apollonian Circle Packings: Number Theory
• The sensual Apollonian circle packing