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arXiv · 2001.05866

Spinors, lattices, and classification of integral Apollonian disk packings

Jerzy Kocik
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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.

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Jerzy Kocik. 2020-01-15. Spinors, lattices, and classification of integral Apollonian disk packings. https://arxiv.org/abs/2001.05866

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