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This paper investigates the behaviour of the kissing number $kappa(n, r)$ of congruent radius $r > 0$ spheres in $mathbb{S}^n$, for $ngeq 2$. Such a quantity depends on the radius $r$, and we plot the approximate graph of $kappa(n, r)$ with relatively high accuracy by using new upper and lower bounds that are produced via semidefinite programming and by using spherical codes, respectively.
This paper provides upper and lower bounds on the kissing number of congruent radius $r > 0$ spheres in $mathbb{H}^n$, for $ngeq 2$. For that purpose, the kissing number is replaced by the kissing function $kappa(n, r)$ which depends on the radius $r
In this note, we give a short solution of the kissing number problem in dimension three.
The average kissing number of $mathbb{R}^n$ is the supremum of the average degrees of contact graphs of packings of finitely many balls (of any radii) in $mathbb{R}^n$. We provide an upper bound for the average kissing number based on semidefinite pr
This paper provides upper and lower bounds on the kissing number of congruent radius $r > 0$ spheres in hyperbolic $mathbb{H}^n$ and spherical $mathbb{S}^n$ spaces, for $ngeq 2$. For that purpose, the kissing number is replaced by the kissing functio
In 1969, Fejes Toth conjectured that in Euclidean 3-space any packing of equal balls such that each ball is touched by twelve others consists of hexagonal layers. This article verifies this conjecture.