New lower bound on ball packing density in high-dimensional hyperbolic spaces
Combinatorics
2024-09-27 v2 Metric Geometry
Abstract
We present a new lower bound on the Bowen-Radin maximal density of radius-R ball packings in the m-dimensional hyperbolic space, improving on the basic covering bound by factor \Omega(m(R+\ln m)) as m tends to infinity. This is done by applying the recent theorem of Campos, Jenssen, Michelen and Sahasrabudhe on independent sets in graphs with sparse neighbourhoods.
Cite
@article{arxiv.2405.07818,
title = {New lower bound on ball packing density in high-dimensional hyperbolic spaces},
author = {Irene Gil Fernández and Jaehoon Kim and Hong Liu and Oleg Pikhurko},
journal= {arXiv preprint arXiv:2405.07818},
year = {2024}
}
Comments
18 pages, minor revision