Exponential improvements for superball packing upper bounds
Copyright policy )Exponential improvements for superball packing upper bounds
We prove that for all fixed $p > 2$, the translative packing density of unit $\ell_p$-balls in $\mathbb{R}^n$ is at most $2^{(γ_p + o(1))n}$ with $γ_p < - 1/p$. This is the first exponential improvement in high dimensions since van der Corput and Schaake (1936).
- Massachusetts Institute of Technology United States
- Stanford University United States
- Massachusetts Institute of Technology Dept. of Economics United States
maximal density, \(l_p\)-ball, translative sphere packing, Mathematics - Metric Geometry, FOS: Mathematics, Packing and covering in \(n\) dimensions (aspects of discrete geometry), Mathematics - Combinatorics, Metric Geometry (math.MG), Combinatorics (math.CO)
maximal density, \(l_p\)-ball, translative sphere packing, Mathematics - Metric Geometry, FOS: Mathematics, Packing and covering in \(n\) dimensions (aspects of discrete geometry), Mathematics - Combinatorics, Metric Geometry (math.MG), Combinatorics (math.CO)
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