Fetching the paper…
Reading the bibliography…
We formulate explicit predictions concerning the symmetry of optimal codes in compact metric spaces.
L. Fejes Tóth, Über die dichteste Kugellagerung, Math. Z. 48 (1940) 676–684
1940
Earlier work this paper cites.
H. E. Salzer, The approximation of numbers as sums of reciprocals, Amer. Math. Monthly 54 (1947) 135–142
1947
Earlier work this paper cites.
H. Davenport, Gy. Hajós, Problem 35 (Hungarian), Mat. Lapok 2 (1951), no. 1, 68
1951
Earlier work this paper cites.
R. A. Rankin, The closest packing of spherical caps in n n dimensions, Glasgow Math. J. 2 (1955) 139–144
1955
Earlier work this paper cites.
N. Oler, A finite packing problem, Can. Math. Bull. 4 (1961) 153–155
1961
Earlier work this paper cites.
R. M. Robinson, Arrangement of 24 24 circles on a sphere, Math. Ann. 144 (1961) 17–48
1961
Earlier work this paper cites.
L. Fejes Tóth, Regular figures, Pergamon, 1964
1964
Earlier work this paper cites.
E. S. Barnes, N. J. A. Sloane, New lattice packings of spheres, Can. J. Math. 35 (1983) 117–130
1983
Earlier work this paper cites.
L. Fejes Tóth, Symmetry induced by economy., Symmetry (1986) 83–91
1986
Earlier work this paper cites.
H. Melissen, Densest packings of congruent circles in an equilateral triangle, Amer. Math. Monthly 100 (1993) 916–925
1993
Earlier work this paper cites.
B. D. Lubachevsky, R. L. Graham, F. H. Stillinger, Patterns and structures in disk packings, Period. Math. Hung. 34 (1997) 123–142
1997
Earlier work this paper cites.
S. Smale, Mathematical Problems for the Next Century, Math. Intelligencer 20 (1998) 7–15
1998
Earlier work this paper cites.
J. H. Conway, N. J. A. Sloane, Sphere packings, lattices and groups, 3rd ed., Springer, 1999
1999
Cited alongside, same era.
T. Ericson, V. Zinoviev, Codes on Euclidean spheres, Elsevier, 2001
2001
Cited alongside, same era.
J. H. Conway, D. A. Smith, On quaternions and octonions, CRC Press, 2003
2003
Cited alongside, same era.
H. Cohn, A. Kumar, Universally optimal distribution of points on spheres, J. Amer. Math. Soc. 20 (2007) 99–148
2007
Cited alongside, same era.
W. Kuperberg, Optimal Arrangements in Packing Congruent Balls in a Spherical Container, Discrete Comput. Geom. 37 (2007) 205–212
2007
Cited alongside, same era.
B. Ballinger, G. Blekherman, H. Cohn, N. Giansiracusa, E. Kelly, A. Schürmann, Experimental study of energy-minimizing point configurations on spheres, Exp. Math. 18 (2009) 257–283
O. R. Musin, A. S. Tarasov, The Tammes problem for N = 14 N=14 , Exp. Math. 24 (2015) 460–468
2015
Later among the works it cites.
O. R. Musin, A. V. Nikitenko, Optimal packings of congruent circles on a square flat torus, Discrete Comput. Geom. 55 (2016) 1–20
2016
Later among the works it cites.
H. Cohn, A. Kumar, S. D. Miller, D. Radchenko, M. Viazovska, The sphere packing problem in dimension 24 24 , Ann. Math. (2017) 1017–1033
2017
Later among the works it cites.
M. S. Viazovska, The sphere packing problem in dimension 8 8 , Ann. Math. (2017) 991–1015
2017
Later among the works it cites.
A. D. N. J. de Grey, The chromatic number of the plane is at least 5, Geombinatorics 28 (2018) 18–31
2018
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2009
Cited alongside, same era.
Gy. Elekes, M. Sharir, Incidences in three dimensions and distinct distances in the plane, SoCG 2010, 413–422
2010
Cited alongside, same era.
M. D. Sikirić, A. Schürmann, F. Vallentin, The contact polytope of the Leech lattice, Discrete Comput. Geom. 44 (2010) 904–911
2010
Cited alongside, same era.
W. Dickinson, D. Guillot, A. Keaton, S. Xhumari, Optimal packings of up to six equal circles on a triangular flat torus, J. Geom. 102 (2011) 27–51
2011
Cited alongside, same era.
T. Tao, Higher order Fourier analysis, Amer. Math. Soc., 2012
2012
Cited alongside, same era.
R. Connelly, W. Dickinson, Periodic planar disc packings, Philos. Trans. R. Soc. A 372 (2014) 20120039
2014
Cited alongside, same era.
L. Guth, N. H. Katz, On the Erdős distinct distance problem in the plane, Ann. Math. (2015) 155–190
2015
Cited alongside, same era.
2018
Later among the works it cites.
J. Jasper, E. J. King, D. G. Mixon, Game of Sloanes: Best known packings in complex projective space, Proc. SPIE, Wavelets and Sparsity XVIII, vol. 11138 (2019) 111381E
2019
Later among the works it cites.
G. S. Kopp, SIC-POVMs and the Stark conjectures, Int. Math. Res. Not. (2021) 13812–13838
2021
Closest in time.
J. W. Iverson, D. G. Mixon, Doubly transitive lines I: Higman pairs and roux, J. Combin. Theory, Ser. A 185 (2022) 105540
2022
Closest in time.
J. W. Iverson, D. G. Mixon, Doubly transitive lines II: Almost simple symmetries, Alg. Combin. 7 (2024) 37–76
2024
Closest in time.