A Lower Bound for the Translative Kissing Numbers of Simplices

( K ) of a d -dimensional convex body K is the maximum number of mutually non-overlapping translates of K that can be arranged so that all touch K . In this paper we show that holds for any d -dimensional simplex ( ). We also prove similar inequalities for some, more general classes of convex bodies.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42312/1/493-20-2-281_00200281.pd

On the lower bound for kissing numbers of ℓp\ell_p-spheres in high dimensions

In this paper, we give some new lower bounds for the kissing number of $\ell_p$-spheres. These results improve the previous work due to Xu (2007). Our method is based on coding theory.Comment: 15 pages, 4 figures; any comments are welcom