-
1
-
-
0012952893
-
An extremal property of the icosahedron
-
N. N. Andreev, An extremal property of the icosahedron, East J. Approx. 2 (1996), 459-462.
-
(1996)
East J. Approx.
, vol.2
, pp. 459-462
-
-
Andreev, N.N.1
-
2
-
-
0043067464
-
Location of points on a sphere with minimal energy
-
N. N. Andreev, Location of points on a sphere with minimal energy, Proc. Steklov Inst. Math. 219 (1997), 20-24.
-
(1997)
Proc. Steklov Inst. Math.
, vol.219
, pp. 20-24
-
-
Andreev, N.N.1
-
3
-
-
84953931627
-
-
Cambridge Tracts in Mathematics 103, Cambridge University Press, Cambridge
-
E. F. Assmus, Jr. and J. D. Key, Designs and Their Codes, Cambridge Tracts in Mathematics 103, Cambridge University Press, Cambridge, 1992.
-
(1992)
Designs and their Codes
-
-
Assmus Jr., E.F.1
Key, J.D.2
-
4
-
-
33646039337
-
Linear programming bounds for codes in grassmannian spaces
-
C. Bachoc, Linear programming bounds for codes in Grassmannian spaces, IEEE Trans. Inform. Theory 52 (2006), 2111-2125.
-
(2006)
IEEE Trans. Inform. Theory
, vol.52
, pp. 2111-2125
-
-
Bachoc, C.1
-
5
-
-
54149083021
-
New upper bounds for kissing numbers from semidef-inite programming
-
C. Bachoc and F. Vallentin, New upper bounds for kissing numbers from semidef-inite programming, J. Amer. Math. Soc. 21 (2008), 909-924.
-
(2008)
J. Amer. Math. Soc.
, vol.21
, pp. 909-924
-
-
Bachoc, C.1
Vallentin, F.2
-
6
-
-
55749105169
-
Optimality and uniqueness of the (4,10, 1/6) spherical code
-
C. Bachoc and F. Vallentin, Optimality and uniqueness of the (4, 10, 1/6) spherical code, J. Combin. Theory Ser. A 116 (2009), 195-204.
-
(2009)
J. Combin. Theory Ser. A
, vol.116
, pp. 195-204
-
-
Bachoc, C.1
Vallentin, F.2
-
7
-
-
84963012034
-
A lower bound for the optimal density of lattice packings
-
K. Ball, A lower bound for the optimal density of lattice packings, Internat. Math. Res. Notices 1992, 217-221.
-
(1992)
Internat. Math. Res. Notices
, pp. 217-221
-
-
Ball, K.1
-
8
-
-
70350031301
-
Experimental study of energy-minimizing point configurations on spheres
-
B. Ballinger, G. Blekherman, H. Cohn, N. Giansiracusa, E. Kelly, and A. Schürmann, Experimental study of energy-minimizing point configurations on spheres, Experiment. Math. 18 (2009), 257-283.
-
(2009)
Experiment. Math.
, vol.18
, pp. 257-283
-
-
Ballinger, B.1
Blekherman, G.2
Cohn, H.3
Giansiracusa, N.4
Kelly, E.5
Schürmann, A.6
-
9
-
-
0001541486
-
Uniqueness of certain spherical codes
-
E. Bannai and N. J. A. Sloane, Uniqueness of certain spherical codes, Canad. J. Math. 33 (1981), 437-449.
-
(1981)
Canad. J. Math.
, vol.33
, pp. 437-449
-
-
Bannai, E.1
Sloane, N.J.A.2
-
10
-
-
0040933747
-
The minimum values of positive quadratic forms in six, seven and eight variables
-
H. F. Blichfeldt, The minimum values of positive quadratic forms in six, seven and eight variables, Math. Z. 39 (1935), 1-15.
-
(1935)
Math. Z.
, vol.39
, pp. 1-15
-
-
Blichfeldt, H.F.1
-
11
-
-
0038310141
-
Densest packing of equal spheres in hyperbolic space
-
L. Bowen and C. Radin, Densest packing of equal spheres in hyperbolic space, Discrete Comput. Geom. 29 (2003), 23-39.
-
(2003)
Discrete Comput. Geom.
, vol.29
, pp. 23-39
-
-
Bowen, L.1
Radin, C.2
-
12
-
-
73649087446
-
Two-dimensional matter: Order, curvature and defects
-
M. Bowick and L. Giomi, Two-dimensional matter: order, curvature and defects, Advances in Physics 58 (2009), 449-563.
-
(2009)
Advances in Physics
, vol.58
, pp. 449-563
-
-
Bowick, M.1
Giomi, L.2
-
13
-
-
0001438198
-
Strongly regular graphs having strongly regular subconstituents
-
P. J. Cameron, J. M. Goethals, and J. J. Seidel, Strongly regular graphs having strongly regular subconstituents, J. Algebra 55 (1978), 257-280.
-
(1978)
J. Algebra
, vol.55
, pp. 257-280
-
-
Cameron, P.J.1
Goethals, J.M.2
Seidel, J.J.3
-
14
-
-
0037909703
-
New upper bounds on sphere packings II
-
H. Cohn, New upper bounds on sphere packings II, Geom. Topol. 6 (2002), 329-353.
-
(2002)
Geom. Topol.
, vol.6
, pp. 329-353
-
-
Cohn, H.1
-
16
-
-
0037769863
-
New upper bounds on sphere packings I
-
H. Cohn and N. D. Elkies, New upper bounds on sphere packings I, Ann. of Math. 157 (2003), 689-714.
-
(2003)
Ann. of Math.
, vol.157
, pp. 689-714
-
-
Cohn, H.1
Elkies, N.D.2
-
17
-
-
34250831282
-
Universally optimal distribution of points on spheres
-
H. Cohn and A. Kumar, Universally optimal distribution of points on spheres, J. Amer. Math. Soc. 20 (2007), 99-148.
-
(2007)
J. Amer. Math. Soc.
, vol.20
, pp. 99-148
-
-
Cohn, H.1
Kumar, A.2
-
18
-
-
71649112588
-
Optimality and uniqueness of the leech lattice among lattices
-
H. Cohn and A. Kumar, Optimality and uniqueness of the Leech lattice among lattices, Ann. of Math. 170 (2009), 1003-1050.
-
(2009)
Ann. of Math.
, vol.170
, pp. 1003-1050
-
-
Cohn, H.1
Kumar, A.2
-
19
-
-
73649140988
-
Ground states and formal duality relations in the Gaussian core model
-
61116
-
H. Cohn, A. Kumar, and A. Schürmann, Ground states and formal duality relations in the Gaussian core model, Phys. Rev. E 80 (2009), 061116:1-7.
-
(2009)
Phys. Rev. E
, vol.80
, pp. 1-7
-
-
Cohn, H.1
Kumar, A.2
Schürmann, A.3
-
22
-
-
51249169208
-
What are all the best sphere packings in low dimensions?
-
J. H. Conway and N. J. A. Sloane, What are all the best sphere packings in low dimensions?, Discrete Comput. Geom. 13 (1995), 383-403.
-
(1995)
Discrete Comput. Geom.
, vol.13
, pp. 383-403
-
-
Conway, J.H.1
Sloane, N.J.A.2
-
23
-
-
0030519411
-
Packing lines, planes, etc.: Packings in grassmannian spaces
-
J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Packing lines, planes, etc.: packings in Grassmannian spaces, Experiment. Math. 5 (1996), 139-159.
-
(1996)
Experiment. Math.
, vol.5
, pp. 139-159
-
-
Conway, J.H.1
Hardin, R.H.2
Sloane, N.J.A.3
-
24
-
-
4344671441
-
-
Sphere Packings, Lattices and Groups, third edition Springer, New York
-
J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, third edition, Grundlehren der Mathematischen Wissenschaften 290, Springer, New York, 1999.
-
(1999)
Grundlehren der Mathematischen Wissenschaften
, vol.290
-
-
Conway, J.H.1
Sloane, N.J.A.2
-
25
-
-
0015357424
-
Bounds for unrestricted codes, by linear programming
-
P. Delsarte, Bounds for unrestricted codes, by linear programming, Philips Res. Rep. 27 (1972), 272-289.
-
(1972)
Philips Res. Rep.
, vol.27
, pp. 272-289
-
-
Delsarte, P.1
-
26
-
-
65649140960
-
Spherical codes and designs
-
P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geom. Dedicata 6 (1977), 363-388.
-
(1977)
Geom. Dedicata
, vol.6
, pp. 363-388
-
-
Delsarte, P.1
Goethals, J.M.2
Seidel, J.J.3
-
27
-
-
0041637573
-
A brownian-motion model for the eigenvalues of a random matrix
-
F. J. Dyson, A Brownian-motion model for the eigenvalues of a random matrix, J. Math. Phys. 3 (1962), 1191-1198.
-
(1962)
J. Math. Phys.
, vol.3
, pp. 1191-1198
-
-
Dyson, F.J.1
-
28
-
-
0004230986
-
-
Pergamon Press, Macmillan, New York
-
L. Fejes Tóth, Regular Figures, Pergamon Press, Macmillan, New York, 1964.
-
(1964)
Regular Figures
-
-
Fejes Tóth, L.1
-
29
-
-
0000491573
-
Cannonballs and honeycombs
-
T. C. Hales, Cannonballs and honeycombs, Notices Amer. Math. Soc. 47 (2000), 440-449.
-
(2000)
Notices Amer. Math. Soc.
, vol.47
, pp. 440-449
-
-
Hales, T.C.1
-
30
-
-
22044441063
-
A proof of the kepler conjecture
-
T. C. Hales, A proof of the Kepler conjecture, Ann. of Math. 162 (2005), 1065-1185.
-
(2005)
Ann. of Math.
, vol.162
, pp. 1065-1185
-
-
Hales, T.C.1
-
31
-
-
0040339737
-
The ubiquity of coxeter-dynkin diagrams (an introduction to the A-D-E problem)
-
M. Hazewinkel, W. Hesselink, D. Siersma, and F. D. Veldkamp, The ubiquity of Coxeter-Dynkin diagrams (an introduction to the A-D-E problem), Nieuw Arch. Wisk. 25 (1977), 257-307.
-
(1977)
Nieuw Arch. Wisk.
, vol.25
, pp. 257-307
-
-
Hazewinkel, M.1
Hesselink, W.2
Siersma, D.3
Veldkamp, F.D.4
-
34
-
-
0004067067
-
-
second edition, Dover Publications, Inc., New York
-
F. Klein, Lectures on the Icosahedron and the Solution of Equations of the Fifth Degree, second edition, Dover Publications, Inc., New York, 1956.
-
(1956)
Lectures on the Icosahedron and the Solution of Equations of the Fifth Degree
-
-
Klein, F.1
-
35
-
-
38349154441
-
On the korkin-zolotarev construction
-
A. V. Kolushov and V. A. Yudin, On the Korkin-Zolotarev construction, Discrete Math. Appl. 4 (1994), 143-146.
-
(1994)
Discrete Math. Appl.
, vol.4
, pp. 143-146
-
-
Kolushov, A.V.1
Yudin, V.A.2
-
36
-
-
0012952662
-
Extremal dispositions of points on the sphere
-
A. V. Kolushov and V. A. Yudin, Extremal dispositions of points on the sphere, Anal. Math. 23 (1997), 25-34.
-
(1997)
Anal. Math.
, vol.23
, pp. 25-34
-
-
Kolushov, A.V.1
Yudin, V.A.2
-
37
-
-
0141517272
-
A comparison of the sherali-adams, lovász-schrijver, and lasserre relaxations for 0-1 programming
-
M. Laurent, A comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre relaxations for 0-1 programming, Math. Oper. Res. 28 (2003), 470-496.
-
(2003)
Math. Oper. Res.
, vol.28
, pp. 470-496
-
-
Laurent, M.1
-
38
-
-
0001654568
-
Notes on sphere packings
-
J. Leech, Notes on sphere packings, Canad. J. Math. 19 (1967), 251-267.
-
(1967)
Canad. J. Math.
, vol.19
, pp. 251-267
-
-
Leech, J.1
-
39
-
-
0038247240
-
On bounds for packings in n-dimensional euclidean space
-
V. I. Levenshtein, On bounds for packings in n-dimensional Euclidean space, Soviet Math. Dokl. 20 (1979), 417-421.
-
(1979)
Soviet Math. Dokl.
, vol.20
, pp. 417-421
-
-
Levenshtein, V.I.1
-
40
-
-
34249842879
-
Designs as maximum codes in polynomial metric spaces
-
V. I. Levenshtein, Designs as maximum codes in polynomial metric spaces, Acta Appl. Math. 29 (1992), 1-82.
-
(1992)
Acta Appl. Math.
, vol.29
, pp. 1-82
-
-
Levenshtein, V.I.1
-
41
-
-
0008239584
-
Fun with hard spheres
-
Wuppertal Lecture Notes in Phys. Springer, New York
-
H. Löwen, Fun with hard spheres, in Statistical Physics and Spatial Statistics (Wuppertal, 1999), 295-331, Lecture Notes in Phys. 554, Springer, New York, 2000.
-
(1999)
Statistical Physics and Spatial Statistics
, vol.554
, pp. 295-331
-
-
Löwen, H.1
-
42
-
-
49749124954
-
The kissing number in four dimensions
-
O. Musin, The kissing number in four dimensions, Ann. of Math. 168 (2008), 1-32.
-
(2008)
Ann. of Math.
, vol.168
, pp. 1-32
-
-
Musin, O.1
-
43
-
-
0001179224
-
New bounds on the number of unit spheres that can touch a unit sphere in n dimensions
-
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 Ser. A 26 (1979), 210-214.
-
(1979)
J. Combin. Theory Ser. A
, vol.26
, pp. 210-214
-
-
Odlyzko, A.M.1
Sloane, N.J.A.2
-
44
-
-
2942657646
-
Symmetric infor-mationally complete quantum measurements
-
J. M. Renes, R. Blume-Kohout, A. J. Scott, and C. M. Caves, Symmetric infor-mationally complete quantum measurements, J. Math. Phys. 45 (2004), 2171-2180.
-
(2004)
J. Math. Phys.
, vol.45
, pp. 2171-2180
-
-
Renes, J.M.1
Blume-Kohout, R.2
Scott, A.J.3
Caves, C.M.4
-
45
-
-
0001878701
-
Positive definite functions on spheres
-
I. J. Schoenberg, Positive definite functions on spheres, Duke Math. J. 9 (1942), 96-107.
-
(1942)
Duke Math. J.
, vol.9
, pp. 96-107
-
-
Schoenberg, I.J.1
-
46
-
-
23844454333
-
New code upper bounds from the terwilliger algebra and semidefinite programming
-
A. Schrijver, New code upper bounds from the Terwilliger algebra and semidefinite programming, IEEE Trans. Inform. Theory 51 (2005), 2859-2866.
-
(2005)
IEEE Trans. Inform. Theory
, vol.51
, pp. 2859-2866
-
-
Schrijver, A.1
-
47
-
-
34250943898
-
Das Problem der dreizehn Kugeln
-
K. Schütte and B. L. van der Waerden, Das Problem der dreizehn Kugeln, Math. Ann. 125 (1953), 325-334.
-
(1953)
Math. Ann.
, vol.125
, pp. 325-334
-
-
Schütte, K.1
Van Der Waerden, B.L.2
-
49
-
-
0000388463
-
On the structure of the atom
-
J. J. Thomson, On the structure of the atom, Phil. Mag. 7 (1904), 237-265.
-
(1904)
Phil. Mag.
, vol.7
, pp. 237-265
-
-
Thomson, J.J.1
-
51
-
-
33750536978
-
New conjectural lower bounds on the optimal density of sphere packings
-
S. Torquato and F. Stillinger, New conjectural lower bounds on the optimal density of sphere packings, Experiment. Math. 15 (2006), 307-331.
-
(2006)
Experiment. Math.
, vol.15
, pp. 307-331
-
-
Torquato, S.1
Stillinger, F.2
-
53
-
-
24144463490
-
Uniqueness of classes of positive quadratic forms on which values of the hermite constant are attained for 6 ≤ n ≤ 8
-
N. M. Vetčinkin, Uniqueness of classes of positive quadratic forms on which values of the Hermite constant are attained for 6 ≤ n ≤ 8, Proc. Steklov Inst. Math. 152 (1982), 37-95.
-
(1982)
Proc. Steklov Inst. Math.
, vol.152
, pp. 37-95
-
-
Vetčinkin, N.M.1
-
54
-
-
33745509190
-
A counterexample to kelvin's conjecture on minimal surfaces
-
D. Weaire and R. Phelan, A counterexample to Kelvin's conjecture on minimal surfaces, Phil. Mag. Lett. 69 (1994), 107-110.
-
(1994)
Phil. Mag. Lett.
, vol.69
, pp. 107-110
-
-
Weaire, D.1
Phelan, R.2
-
55
-
-
84961471236
-
Minimum potential energy of a point system of charges
-
V. A. Yudin, Minimum potential energy of a point system of charges, Discrete Math. Appl. 3 (1993), 75-81.
-
(1993)
Discrete Math. Appl.
, vol.3
, pp. 75-81
-
-
Yudin, V.A.1
|