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New lower bound on ball packing density in high-dimensional hyperbolic spaces

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arxiv 2405.07818 v2 pith:CD3I6LPT submitted 2024-05-13 math.CO math.MG

Irene Gil Fernández , Jaehoon Kim , Hong Liu , Oleg Pikhurko This is my paper · ORCID
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keywords boundballdensityhyperboliclowerapplyingbasicbowen-radin
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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.

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  1. Linear programming bounds in homogeneous spaces, I: Optimal packing density

    math.MG 2025-05 conditional novelty 7.0 of 10

    Linear programming upper bounds for sphere packing densities are proven for homogeneous spaces, including a hyperbolic bound conjectured by Cohn and Zhao.

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