A125847 Denominator of volume of best symplectic packing of n balls in 4-dimensional ball.

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

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 blow-up 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