A. Aliev

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20222025

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math.MG2022

On the Packing Density Bound in 3-Space

Arkadiy Aliev

The note shows an easy way to improve E.H. Smith's packing density bound in $R^{3}$ from $0.53835...$ to $0.54755...$ .

math.MG2022

New estimates for $d_{2, 1}$ and $d_{3, 2}$

Arkadiy Aliev

Let $K$ be a convex body in $R^{n}$ . Let $d_{n, n - 1} (K)$ be the smallest possible density of a non-separable lattice of translates of $K$ . In this paper we prove the estim…

On the Packing Density Bound in 3-Space

New estimates for d2,1​ and d3,2​

New estimates for $d_{2, 1}$ and $d_{3, 2}$