Density of Binary Disc Packings: The 9 Compact Packings
Discrete Mathematics
2021-05-04 v3 Metric Geometry
Abstract
A disc packing in the plane is compact if its contact graph is a triangulation. There are values of such that a compact packing by discs of radii and exists. We prove, for each of these values, that the maximal density over all the packings by discs of radii and is reached for a compact packing (we give it as well as its density).
Cite
@article{arxiv.2002.07168,
title = {Density of Binary Disc Packings: The 9 Compact Packings},
author = {Nicolas Bédaride and Thomas Fernique},
journal= {arXiv preprint arXiv:2002.07168},
year = {2021}
}
Comments
code (SageMath) included in the source archive. arXiv admin note: text overlap with arXiv:1912.02297