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A173715
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Number of minimally rigid n x n adjacency matrices of sphere packings in R^3.
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2
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OFFSET
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1,6
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..10.
Natalie Arkus, Vinothan N. Manoharan, Michael P. Brenner. Deriving Finite Sphere Packings, Nov 24, 2010.
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CROSSREFS
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Cf. A000088, A006125, A174423, A174424.
Sequence in context: A210526 A221079 A162287 * A166168 A126559 A213795
Adjacent sequences: A173712 A173713 A173714 * A173716 A173717 A173718
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KEYWORD
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nonn,hard
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AUTHOR
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Jonathan Vos Post, Nov 25 2010
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STATUS
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approved
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