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Search: id:A133587
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| A133587 |
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Conjectured order of the symmetry group of the (numerically computed) least-perimeter cluster of n nonoverlapping circles. |
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+0
1
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| 4, 6, 4, 2, 10, 12, 14, 2, 4, 2, 6, 2, 4, 1, 2, 2, 2, 12, 2, 2, 1
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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This can be thought of as the order of the symmetry group of the minimum-energy configuration of n two-dimensional bubbles in a plane. a(1) is infinite, because one bubble forms a circle, which has a continuous symmetry group containing rotations of arbitrary angles. So far, the actual symmetry groups are all dihedral, except for a(15) and a(22), which are trivial (their configurations have no symmetries).
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REFERENCES
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Cox, S. J., F. Graner, M. F. Vaz, C. Monnereau-Pittet, and N. Pittet, 2003, Minimal perimeter for N identical bubbles in two dimensions: calculations and simulations, Philos. Mag. 83, 1393-1406.
F. Morgan, Soap bubble clusters, Rev. Mod. Phys. Vol. 79 (2007), pp. 821-827.
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LINKS
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R. L. Graham and N. J. A. Sloane, Penny-Packing and Two-Dimensional Codes, Discrete and Comput. Geom. 5 (1990), 1-11.
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EXAMPLE
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a(3) = 6 because three planar bubbles arrange themselves in an equilateral-triangle-type configuration with symmetry group D_3, of order 6.
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CROSSREFS
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Cf. A133491.
Sequence in context: A062751 A135911 A001138 this_sequence A128633 A001482 A078385
Adjacent sequences: A133584 A133585 A133586 this_sequence A133588 A133589 A133590
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KEYWORD
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nonn
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AUTHOR
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Keenan Pepper (keenanpepper(AT)gmail.com), Dec 27 2007
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