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

2025/05/29 by Wackenhuth, Maximilian
#FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG) #Probability (math.PR)

paper · doi:10.48550/arxiv.2505.23572

Abstract

In this article we obtain linear programming bounds for the maximal sphere packing density of commutative spaces. A special case of our results solves a conjecture by Cohn and Zhao on linear programming bounds for sphere packings in hyperbolic space.

Citations

• Bounds on hyperbolic sphere packings: On a conjecture by Cohn and Zhao
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• Fourier transforms of spherical distributions on compact symmetric spaces
• Gelfand pairs on the Heisenberg group and Schwartz functions
• The ergodic theory of lattice subgroups
• Periodicity and Circle Packing in the Hyperbolic Plane
• Optimally dense packings of hyperbolic space

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• Bounds on hyperbolic sphere packings: On a conjecture by Cohn and Zhao
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• Dual Linear Programming Bounds for Sphere Packing via Discrete Reductions
• Sphere packing bounds via rescaling