

A125847


Denominator of volume of best symplectic packing of n balls in 4dimensional ball.


4



1, 2, 4, 1, 5, 25, 64, 289, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
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OFFSET

1,2


COMMENTS

Explanation, figure, table, references in Traynor. McDuff and Polterovich's existence proof of these packings in nonexplicit; they result from the symplectic blowup operation. Explicit constructions for n = 8 and n = 9 are still unknown. Biran showed that A125846(n) = A125847(n) = 1 for all n>9.


REFERENCES

See A125846 for references.


LINKS

Table of n, a(n) for n=1..92.


FORMULA

A125846(n)/a(n) is maximal symplectic packing density with n balls, as calculated by McDuff and Polterovich.


EXAMPLE

For n = 1..9, densities are 1, 1/2, 3/4, 1, 4/5, 24/25, 63/64, 288/289, 1.


CROSSREFS

Cf. A125846.
See A030042/A030043 for an unreduced version.
Sequence in context: A090285 A286784 A047908 * A078886 A307796 A095247
Adjacent sequences: A125844 A125845 A125846 * A125848 A125849 A125850


KEYWORD

nonn,frac


AUTHOR

Jonathan Vos Post, Dec 11 2006.


EXTENSIONS

Edited by N. J. A. Sloane, Feb 12 2021


STATUS

approved



