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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: A016734 A272473 A362270 * 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 August 4 01:12 EDT 2024. Contains 374905 sequences. (Running on oeis4.)