Also interesting would be to maximize the sum of the pth power of the diameters, for N = 1,2,3,.... I wonder if for some given N the maximizing configuration changes discontinuously as p goes past some value p_0. —Dan
On Feb 19, 2016, at 6:08 AM, Veit Elser <ve10@cornell.edu> wrote:
On Feb 19, 2016, at 8:48 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
I'm a tad suspicious: are the circle packings on Friedman's page proved to be maximal, or are they merely the best known so far? There is no link to any proofs, or key to diameters … WFL
I have a conjecture that the maximum-sum-of-diameters packings have triangulated contact graphs. If that’s true, one could enumerate the graphs and calculate the packing for each one to see which is maximal.
-Veit
http://mathoverflow.net/questions/38086/a-circle-packing-conjecture