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21 votes
1 answer
1k views

Sphere packings : what next after the recent breakthrough of Viazovska (et al.)?

Given the march 2016 breakthrough concerning sphere packings by Viazovska for the case of dimension 8, and by Cohn, Kumar, Miller, Radchenko and Viazovska for the case of dimension 24, it follows that ...
Archie's user avatar
  • 883
3 votes
1 answer
118 views

Question arise from kissing number in 2 dimension

I'm considering an extended problem of kissing number in $\mathbb{R}^2$. Suppose I have a given disc $\mathcal{D}$ of radius 1/2 and infinitely many discs all of radius 1/2 and all these discs and ...
neverevernever's user avatar
2 votes
1 answer
588 views

Kissing number lower bound vs. upper bound - precise meanings?

According to en.wikipedia.org, https://en.wikipedia.org/wiki/Kissing_number#Some_known_bounds It says the kissing numbers $K$ have lower bound $K_L$ and upper bound $K_S$: $$ K_L < K < K_U. $$ I ...
zeta's user avatar
  • 447