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Original Articles

The Tammes Problem for N = 14

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REFERENCES

  • [Aigner and Ziegler 98/02] M. Aigner and G. M. Ziegler. Proofs from THE BOOK. Berlin Heidelberg: Springer-Verlag, 1998 (First edition) and 2002 (Second edition).
  • >[Anstreicher 04] K. Anstreicher. “The Thirteen Spheres: A New Proof.” Discr. Comput. Geom. 31 (2004), 613–625.
  • [Bachoc and Vallentin 08] C. Bachoc and F. Vallentin. “New Upper Bounds for Kissing Numbers from Semidefinite Programming.” J. Am. Math. Soc. 21 (2008), 909–924.
  • [Böröczky 83] K. Böröczky. “The Problem of Tammes for n = 11.” Studi. Sci. Math. Hungar. 18 (1983), 165–171.
  • [Böröczky 03] K. Böröczky. “The Newton-Gregory Problem Revisited.” In Discrete Geometry, edited by A. Bezdek, pp. 103–110. New York, NY: Marcel Dekker, 2003.
  • [Böröczky and Szabó 03] K. Böröczky and L. Szabó. “Arrangements of 13 Points on a Sphere.” In Discrete Geometry, edited by A. Bezdek, pp. 111–184. New York, NY: Marcel Dekker, 2003.
  • [Böröczky and Szabó 03] K. Böröczky and L. Szabó. “Arrangements of 14, 15, 16 and 17 Points on a Sphere.” Studi. Sci. Math. Hung. 40 (2003), 407–421.
  • [Boyd and Vandenberghe 04] S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge: Cambridge University Press, 2004.
  • [Brass et al. 05] P. Brass, W. O. J. Moser, and J. Pach. Research Problems in Discrete Geometry. New York, NY: Springer-Verlag, 2005.
  • [Brinkmann and McKay] G. Brinkmann and B. D. McKay. Fast Generation of Planar Graphs ( Expanded edition). Commun. Math. Comput. Chem. 58 (2007), 323–357.
  • [Connelly 05] R. Connelly. “Generic Global Rigidity.” Discr. Comput. Geom. 33: 4 (2005), 549–563.
  • [Danzer 86] L. Danzer. “Finite Point-Sets on S2 with Minimum Distance as Large as Possible.” Discr. Math. 60 (1986), 3–66.
  • [Fejes Tóth 43] L. Fejes Tóth. “Über die Abschätzung des kürzesten Abstandes zweier Punkte eines auf einer Kugelfläche liegenden Punktsystems.” Jber. Deutch. Math. Verein. 53 (1943), 66–68.
  • [Fejes Tóth 53] L. Fejes Tóth. Lagerungen in der Ebene, auf der Kugel und in Raum. Berlin Heidelberg: Springer-Verlag, 1953. Russian translation, Moscow, 1958.
  • [Hsiang 01] W.-Y. Hsiang. Least Action Principle of Crystal Formation of Dense Packing Type and Kepler’s Conjecture. Nankai Tracts in Mathematics 3, River Edge, NJ: World Scientific Publishing Co. Inc., 2001.
  • [Leech 56] J. Leech. “The Problem of the Thirteen Spheres.” Math. Gazette 41 (1956), 22–23.
  • [Levenshtein 79] V. I. Levenshtein. “On Bounds for Packing in n-Dimensional Euclidean Space.” Sov. Math. Dokl. 20: 2 (1979), 417–421.
  • [Maehara 01] H. Maehara. “Isoperimetric Theorem for Spherical Polygons and the Problem of 13 Spheres.” Ryukyu Math. J. 14 (2001), 41–57.
  • [Maehara 07] H. Maehara. “The Problem of Thirteen Spheres – A Proof for Undergraduates.” Eur. J. Combin. 28 (2007), 1770–1778.
  • [Musin 06] O. R. Musin. “The Kissing Problem in Three Dimensions.” Discr. Comput. Geom. 35 (2006), 375–384.
  • [Musin 08] O. R. Musin. “The Kissing Number in Four Dimensions.” Ann. Math. 168 (2008), 1–32.
  • [Musin and Tarasov 12] O. R. Musin and A. S. Tarasov. “The Strong Thirteen Spheres Problem.” Discr. Comput. Geom. 48 (2012), 128–141.
  • [Musin and Tarasov 13] O. R. Musin and A. S. Tarasov. “Enumeration of Irreducible Contact Graphs on the Sphere.” Fundam. Prikl. Mat. 18: 2 (2013), 125–145.
  • [Odlyzko and Sloane 79] A. M. Odlyzko and N. J. A. Sloane. “New Bounds on the Number of Unit Spheres That Can Touch a Unit Sphere in n Dimensions.” J. Combin. Theory A 26 (1979), 210–214.
  • [plantri] plantri (Version 4.5) Available at http://cs.anu.edu.au/~bdm/~plantri/. (Accessed Sep. 5, 2011).
  • [Pfender and Ziegler 04] F. Pfender and G. M. Ziegler. “Kissing Numbers, Sphere Packings, and Some Unexpected Proofs.” Notices Am. Math. Soc. 51 (2004), 873–883.
  • [Robinson 61] R. M. Robinson. “Arrangement of 24 Circles on a Sphere.” Math. Ann. 144 (1961), 17–48.
  • [Schütte and van der Waerden 51] K. Schütte and B. L. van der Waerden. “Auf welcher Kugel haben 5,6,7,8 oder 9 Punkte mit Mindestabstand 1 Platz?” Math. Ann. 123 (1951), 96–124.
  • [Schütte and van der Waerden 53] K. Schütte and B. L. van der Waerden. “Das Problem der dreizehn Kugeln.” Math. Ann. 125 (1953), 325–334.
  • [Tammes 30] R. M. L. Tammes. “On the Origin Number and Arrangement of the Places of Exits on the Surface of Pollengrains.” Rec. Trv. Bot. Neerl. 27 (1930), 1–84.

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