Domains of Convergence for Polyhedral Packings
Number Theory
2021-09-06 v1 Combinatorics
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.
Keywords
Cite
@article{arxiv.2109.01289,
title = {Domains of Convergence for Polyhedral Packings},
author = {Nooria Ahmed and William Ball and Ellis Buckminster and Emilie Rivkin and Dylan Torrance and Jake Viscusi and Runze Wang and Ian Whitehead and S. Yang},
journal= {arXiv preprint arXiv:2109.01289},
year = {2021}
}
Comments
26 pages, 6 figures