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A173715
Number of minimally rigid n x n adjacency matrices of sphere packings in R^3.
2
1, 1, 1, 1, 1, 4, 29, 438, 13828, 750352
OFFSET
1,6
COMMENTS
3rd column of Table 1. The Growth of Adjacency Matrices with n, p.6, of Arkus. 2nd column is A000088 (number of equivalence classes of sign patterns of totally nonzero symmetric n X n matrices). 1st column might be A006125(n) = 2^(n(n-1)/2). We focus on enumerating only minimally rigid sphere packings; which we define as packings with >= 3 contacts per particle and >= 3n - 6 total contacts. Minimal rigidity is necessary, but not sufficient, for a structure to be rigid. Due to the large number of packings that must be evaluated, this analytical method is implemented computationally, and near n = 10 we reach the method's computational limitations.
LINKS
Natalie Arkus, Vinothan N. Manoharan, Michael P. Brenner. Deriving Finite Sphere Packings, Nov 24, 2010.
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
Jonathan Vos Post, Nov 25 2010
STATUS
approved