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arXiv · 2109.01289

Domains of Convergence for Polyhedral Packings

Nooria Ahmed·William Ball·Ellis Buckminster·Emilie Rivkin·Dylan Torrance·Jake Viscusi·Runze Wang·Ian Whitehead·S. Yang
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Abstract

Polyhedral circle packings are generalizations of the Apollonian packing. We develop the theory of the Apollonian group, Descartes quadratic form, and related objects for all polyhedral packings. We use these tools to determine the domain of absolute convergence of a generating function that can be associated to any polyhedral packing. This domain of convergence is the Tits cone for an infinite root system.

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Nooria Ahmed, William Ball, Ellis Buckminster, Emilie Rivkin, Dylan Torrance, Jake Viscusi, Runze Wang, Ian Whitehead, S. Yang. 2021-09-03. Domains of Convergence for Polyhedral Packings. https://arxiv.org/abs/2109.01289

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