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A125846 Numerator of volume of best symplectic packing of n balls in 4-dimensional ball. 4
1, 1, 3, 1, 4, 24, 63, 288, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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

P. Biran, Symplectic packing in dimension 4, Geom. Funct. Anal. 7(1997), 420-437, MR1466333.

D. McDuff and L. Polterovich, Symplectic packings and algebraic geometry, Invent. Math. 115 (1994), 403-434, MR1262938.

Schlenk, Felix. "Dusa McDuff and symplectic geometry." arXiv preprint arXiv:2011.03317 (2020).

Lisa Traynor, Book review (of Embedding problems in symplectic geometry, by Felix Schlenk, deGruyter Expositions in Mathematics, vol. 40, Berlin, 2005), Bull. Amer. Math. Soc. 43 (2006). 593-597.

LINKS

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

FORMULA

A125846(n)/A125847(n) is maximal symplectic packing density with n balls, as calculated by McDuff and Polterovich.

EXAMPLE

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

CROSSREFS

Cf. A125847. See A030042/A030043 for an unreduced version.

Sequence in context: A112668 A016734 A272473 * A318382 A340190 A143677

Adjacent sequences:  A125843 A125844 A125845 * A125847 A125848 A125849

KEYWORD

nonn,frac

AUTHOR

Jonathan Vos Post, Dec 11 2006

EXTENSIONS

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

STATUS

approved

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Last modified June 21 12:19 EDT 2021. Contains 345364 sequences. (Running on oeis4.)