Sphere packings, lattices and groups:
Gespeichert in:
| Beteiligte Personen: | , |
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| Format: | Buch |
| Sprache: | Englisch |
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New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest
Springer-Verlag
1993
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| Ausgabe: | Second edition |
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften
290 |
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| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005401196&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturverz. S. 572 - 656 |
| Umfang: | XLIII, 679 Seiten Illustrationen |
| ISBN: | 0387979123 |
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| 100 | 1 | |a Conway, John Horton |d 1937-2020 |e Verfasser |0 (DE-588)119529289 |4 aut | |
| 245 | 1 | 0 | |a Sphere packings, lattices and groups |c J. H. Conway, N. J. A. Sloane ; with additional contributions by E. Bannai, R.E. Borcherds, J. Leech, S.P. Norton, A.M. Odlyzko, R.A. Parker, L. Queen and B.B. Venkov |
| 250 | |a Second edition | ||
| 264 | 1 | |a New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest |b Springer-Verlag |c 1993 | |
| 300 | |a XLIII, 679 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Grundlehren der mathematischen Wissenschaften |v 290 | |
| 500 | |a Literaturverz. S. 572 - 656 | ||
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| 650 | 4 | |a Groupes finis | |
| 650 | 4 | |a Pavage et remplissage (Géométrie combinatoire) | |
| 650 | 4 | |a Sphère | |
| 650 | 4 | |a Treillis, Théorie des | |
| 650 | 4 | |a Finite groups | |
| 650 | 4 | |a Lattice theory | |
| 650 | 4 | |a Sphere packings | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 052 2001 A 10984(2) |
|---|---|
| DE-BY-TUM_katkey | 600294 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010687042 |
| _version_ | 1821938859804459008 |
| adam_text | Contents
Preface to First Edition v
Preface to Second Edition xv
List of Symbols xxx
Chapter 1
Sphere Packings and Kissing Numbers
J.H. Conway and N.J.A. Sloane I
1. The Sphere Packing Problem 1
1.1 Packing Ball Bearings 1
1.2 Lattice Packings 3
1.3 Nonlattice Packings 7
1.4 « Dimensional Packings 8
1.5 Sphere Packing Problem—Summary of Results 12
2. The Kissing Number Problem 21
2.1 The Problem of the Thirteen Spheres 21
2.2 Kissing Numbers in Other Dimensions 21
2.3 Spherical Codes 24
2.4 The Construction of Spherical Codes from Sphere
Packings 26
2.5 The Construction of Spherical Codes from Binary Codes ... 26
2.6 Bounds on A(n, i ) 27
Appendix: Planetary Perturbations 29
Chapter 2
Coverings, Lattices and Quantizers
J.H. Conway and N.J.A. Sloane 31
1. The Covering Problem 31
1.1 Covering Space with Overlapping Spheres 31
1.2 The Covering Radius and the Voronoi Cells 33
1.3 Covering Problem—Summary of Results 36
1.4 Computational Difficulties in Packings and Coverings 40
xxxiv Contents
2. Lattices, Quadratic Forms and Number Theory 41
2.1 The Norm of a Vector 41
2.2 Quadratic Forms Associated with a Lattice 42
2.3 Theta Series and Connections with Number Theory 44
2.4 Integral Lattices and Quadratic Forms 47
2.5 Modular Forms 50
2.6 Complex and Quaternionic Lattices 52
3. Quantizers 56
3.1 Quantization, Analog to Digital Conversion and Data
Compression 56
3.2 The Quantizer Problem 59
3.3 Quantizer Problem—Summary of Results 59
Chapter 3
Codes, Designs and Groups
J.H. Conway and N.J.A. Sloane 63
1. The Channel Coding Problem 63
1.1 The Sampling Theorem 63
1.2 Shannon s Theorem 66
1.3 Error Probability 69
1.4 Lattice Codes for the Gaussian Channel 71
2. Error Correcting Codes 75
2.1 The Error Correcting Code Problem 75
2.2 Further Definitions from Coding Theory 77
2.3 Repetition, Even Weight and Other Simple Codes 79
2.4 Cyclic Codes 79
2.5 BCH and Reed Solomon Codes 81
2.6 Justesen Codes 82
2.7 Reed Muller Codes 83
2.8 Quadratic Residue Codes 84
2.9 Perfect Codes 85
2.10 The Pless Double Circulant Codes 86
2.11 Goppa Codes and Codes from Algebraic Curves 87
2.12 Nonlinear Codes 87
2.13 Hadamard Matrices 87
3. / Designs, Steiner Systems and Spherical / Designs 88
3.1 / Designs and Steiner Systems 88
3.2 Spherical / Designs 89
4. The Connections with Group Theory 90
4.1 The Automorphism Group of a Lattice 90
4.2 Constructing Lattices and Codes from Groups 92
Chapter 4
Certain Important Lattices and Their Properties
J.H. Conway and N.J.A. Sloane 94
1. Introduction 94
2. Reflection Groups and Root Lattices 95
3. Gluing Theory 99
Contents xxxv
4. Notation; Theta Functions 101
4.1 Jacobi Theta Functions 102
5. The /j Dimensional Cubic Lattice Z 106
6. The /j Dimensional Lattices Aa and A* 108
6.1 The Lattice An 108
6.2 The Hexagonal Lattice 110
6.3 The Face Centered Cubic Lattice 112
6.4 The Tetrahedral or Diamond Packing 113
6.5 The Hexagonal Close Packing 113
6.6 The Dual Lattice A* 115
6.7 The Body Centered Cubic Lattice 116
7. The M Dimensional Lattices Dn and D* 117
7.1 The Lattice £ „ 117
7.2 The Four Dimensional Lattice D4 118
7.3 The Packing D+, 119
7.4 The Dual Lattice D*n 120
8. The Lattices E6, E1 and £g 120
8.1 The 8 Dimensional Lattice £8 120
8.2 The 7 Dimensional Lattices E , and E% 124
8.3 The 6 Dimensional Lattices Eb and E% 125
9. The 12 Dimensional Coxeter Todd Lattice Kl2 127
10. The 16 Dimensional Barnes Wall Lattice A,6 129
11. The 24 Dimensional Leech Lattice A24 131
Chapter 5
Sphere Packing and Error Correcting Codes
J. Leech and N.J.A. Shane 136
1. Introduction 136
1.1 The Coordinate Array of a Point 137
2. Construction A 137
2.1 The Construction 137
2.2 Center Density 137
2.3 Kissing Numbers 138
2.4 Dimensions 3 to 6 138
2.5 Dimensions 7 and 8 138
2.6 Dimensions 9 to 12 139
2.7 Comparison of Lattice and Nonlattice Packings 140
3. ConstructionB 141
3.1 The Construction 141
3.2 Center Density and Kissing Numbers 141
3.3 Dimensions 8, 9 and 12 142
3.4 Dimensions 15 to 24 142
4. Packings Built Up by Layers 142
4.1 Packing by Layers 142
4.2 Dimensions 4 to 7 144
4.3 Dimensions 11 and 13 to 15 144
4.4 Density Doubling and the Leech Lattice A24 145
4.5 Cross Sections of A24 145
5. Other Constructions from Codes 146
xxxvi Contents
5.1 A Code of Length 40 146
5.2 A Lattice Packing in R40 147
5.3 Cross Sections of A^ 148
5.4 Packings Based on Ternary Codes 148
5.5 Packings Obtained from the Pless Codes 148
5.6 Packings Obtained from Quadratic Residue Codes 149
5.7 Density Doubling in R24 and R48 149
6. Construction C 150
6.1 The Construction 150
6.2 Distance Between Centers 150
6.3 Center Density 150
6.4 Kissing Numbers 151
6.5 Packings Obtained from Reed Muller Codes 151
6.6 Packings Obtained from BCH and Other Codes 152
6.7 Density of BCH Packings 153
6.8 Packings Obtained from Justesen Codes 155
Chapter 6
Laminated Lattices
J.H. Conway and N.J.A. Sloane 157
1. Introduction 157
2. The Main Results 163
3. Properties of Ao to A8 168
4. Dimensions 9 to 16 170
5. The Deep Holes in A,6 174
6. Dimensions 17 to 24 176
7. Dimensions 25 to 48 177
Appendix: The Best Integral Lattices Known 179
Chapter 7
Further Connections Between Codes and Lattices
N.J.A. Sloane 181
1. Introduction 181
2. Construction A 182
3. Self Dual (or Type I) Codes and Lattices .; 185
4. Extremal Type I Codes and Lattices 189
5. Construction B 191
6. Type II Codes and Lattices 191
7. Extremal Type II Codes and Lattices 193
8. Constructions A and B for Complex Lattices 197
9. Self Dual Nonbinary Codes and Complex Lattices 202
10. Extremal Nonbinary Codes and Complex Lattices 205
Chapter 8
Algebraic Constructions for Lattices
J.H. Conway and N.J.A. Sloane 206
1. Introduction 206
2. The Icosians and the Leech Lattice 207
Contents xxxvii
2.1 The Icosian Group 207
2.2 The Icosian and Turyn Type Constructions for the Leech
Lattice 210
3. A General Setting for Construction A, and Quebbemann s
64 Dimensional Lattice 211
4. Lattices Over Z[e 4], and Quebbemann s 32 Dimensional
Lattice 215
5. McKay s 40 Dimensional Extremal Lattice 221
6. Repeated Differences and Craig s Lattices 222
7. Lattices from Algebraic Number Theory 224
7.1 Introduction 224
7.2 Lattices from the Trace Norm 224
7.3 Examples from Cyclotomic Fields 227
7.4 Lattices from Class Field Towers 227
7.5 Unimodular Lattices with an Automorphism of Prime
Order 229
8. Constructions D and D 232
8.1 Construction D 232
8.2 Examples 233
8.3 Construction D 235
9. Construction E 236
10. Examples of Construction E 238
Chapter 9
Bounds for Codes and Sphere Packings
N.J.A. Sloane 245
1. Introduction 245
2. Zonal Spherical Functions 249
2.1 The 2 Point Homogeneous Spaces 250
2.2 Representations of G 252
2.3 Zonal Spherical Functions 253
2.4 Positive Definite Degenerate Kernels 256
3. The Linear Programming Bounds 257
3.1 Codes and Their Distance Distributions 257
3.2 The Linear Programming Bounds 258
3.3 Bounds for Error Correcting Codes 260
3.4 Bounds for Constant Weight Codes 263
3.5 Bounds for Spherical Codes and Sphere Packings 263
4. Other Bounds 265
Chapter 10
Three Lectures on Exceptional Groups
J.H. Conway 267
1. First Lecture 267
1.1 Some Exceptional Behavior of the Groups /.„( /) 267
1.2 The Case p = 3 269
1.3 The Case p = 5 269
1.4 The Case p = 7 269
xxxviii Contents
1.5 TheCasep=ll 271
1.6 A Presentation for M12 273
1.7 Janko s Group of Order 175560 273
2. Second Lecture 274
2.1 The Mathieu Group Af24 274
2.2 The Stabilizer of an Octad 276
2.3 The Structure of the Golay Code %24 278
2.4 The Structure of P (ft)/%4 278
2.5 The Maximal Subgroups of M24 279
2.6 The Structure of P(il) 283
3. Third Lecture 286
3.1 The Group Co0 = 0 and Some of its Subgroups 286
3.2 The Geometry of the Leech Lattice 286
3.3 The Group 0 and its Subgroup N 287
3.4 Subgroups of 0 290
3.5 The Higman Sims and McLaughlin Groups 292
3.6 The Group Co, = 3 293
3.7 Involutions in 0 294
3.8 Congruences for Theta Series 294
3.9 A Connection Between 0 and Fischer s Group F/24 295
Appendix: On the Exceptional Simple Groups 296
Chapter 11
The Golay Codes and the Mathieu Groups
J.H. Conway 299
1. Introduction 299
2. Definitions of the Hexacode 300
3. Justification of a Hexacodeword 302
4. Completing a Hexacodeword 302
5. The Golay Code €24and the MOG 303
6. Completing Octads from 5 of their Points 305
7. The Maximal Subgroups of M24 307
8. The Projective Subgroup L2(23) 308
9. The Sextet Group 26:3S6 309
10. The Octad Group 2 : A8 311
11. The Triad Group and the Projective Plane of Order 4 314
12. The Trio Group 26: (S3 x L2(7)) 316
13. The Octern Group 318
14. The Mathieu Group M2i 319
15. The Group M22:2 319
16. The Group Ml2, the Tetracode and the MINIMOG 320
17. Playing Cards and Other Games 323
18. Further Constructions for A/12 327
Chapter 12
A Characterization of the Leech Lattice
J.H. Conway 331
Contents xxxix
Chapter 13
Bounds on Kissing Numbers
A.M. Odlyzko and N.J.A. Sloane 337
1. A General Upper Bound 337
2. Numerical Results 338
Chapter 14
Uniqueness of Certain Spherical Codes
E. Bannai and N.J.A. Sloane 340
1. Introduction 340
2. Uniqueness of the Code of Size 240 in i 342
3. Uniqueness of the Code of Size 56 in fl7 344
4. Uniqueness of the Code of Size 196560 in H24 345
5. Uniqueness of the Code of Size 4600 in n2, 349
Chapter 15
On the Classification of Integral Quadratic Forms
J.H. Conway and N.J.A. Sloane 352
1. Introduction 352
2. Definitions 354
2.1 Quadratic Forms 354
2.2 Forms and Lattices; Integral Equivalence 355
3. The Classification of Binary Quadratic Forms 356
3.1 Cycles of Reduced Forms 356
3.2 Definite Binary Forms 357
3.3 Indefinite Binary Forms 359
3.4 Composition of Binary Forms 364
3.5 Genera and Spinor Genera for Binary Forms 366
4. The p Adic Numbers 366
4.1 The p Adic Numbers 367
4.2 p Adic Square Classes 367
4.3 An Extended Jacobi Legendre Symbol 368
4.4 Diagonalization of Quadratic Forms 369
5. Rational Invariants of Quadratic Forms 370
5.1 Invariants and the Oddity Formula 370
5.2 Existence of Rational Forms with Prescribed Invariants 372
5.3 The Conventional Form of the Hasse Minkowski
Invariant 373
6. The Invariance and Completeness of the Rational
Invariants 373
6.1 The p Adic Invariants for Binary Forms 373
6.2 The p Adic Invariants for « Ary Forms 375
6.3 The Proof of Theorem 7 377
7. The Genus and its Invariants 378
7.1 p Adic Invariants 378
7.2 The p Adic Symbol for a Form 379
xl Contents
7.3 2 Adic Invariants 380
7.4 The 2 Adic Symbol 380
7.5 Equivalences Between Jordan Decompositions 381
7.6 A Canonical 2 Adic Symbol 382
7.7 Existence of Forms with Prescribed Invariants 382
7.8 A Symbol for the Genus 384
8. Classification of Forms of Small Determinant and of
p Elementary Forms 385
8.1 Forms of Small Determinant 385
8.2 p Elementary Forms 386
9. The Spinor Genus 388
9.1 Introduction 388
9.2 The Spinor Genus 389
9.3 Identifying the Spinor Kernel 390
9.4 Naming the Spinor Operators for the Genus of/ 390
9.5 Computing the Spinor Kernel from the p Adic Symbols 391
9.6 Tractable and Irrelevant Primes 392
9.7 When is There Only One Class in the Genus? 393
10. The Classification of Positive Definite Forms 396
10.1 Minkowski Reduction 396
10.2 The Kneser Gluing Method 399
10.3 Positive Definite Forms of Determinant 2 and 3 399
11. Computational Complexity 402
Chapter 16
Enumeration of Unimodular Lattices
J.H. Conway and N.J.A. Sloane 406
1. The Niemeier Lattices and the Leech Lattice 406
2. The Mass Formulae for Lattices 408
3. Verifications of Niemeier s List 410
4. The Enumeration of Unimodular Lattices in Dimensions
n « 23 413
Chapter 17
The 24 Dimensional Odd Unimodular Lattices
R.E. Borcherds 421
Chapter 18
Even Unimodular 24 Dimensional Lattices
B.B. Venkov 427
1. Introduction 427
2. Possible Configurations of Minimal Vectors 428
3. On Lattices with Root Systems of Maximal Rank 431
4. Construction of the Niemeier Lattices 434
5. A Characterization of the Leech Lattice 437
Contents xli
Chapter 19
Enumeration of Extremal Self Dual Lattices
J.H. Conway, A.M. Odlyzko and N.J.A. Shane 439
1. Dimensions 1 16 439
2. Dimensions 17 47 439
3. Dimensions n s 48 441
Chapter 20
Finding the Closest Lattice Point
J.H. Conway and N.J.A. Sloane 443
1. Introduction 443
2. The Lattices Z , Dn and An 444
3. Decoding Unions of Cosets 446
4. Soft Decision Decoding for Binary Codes 447
5. Decoding Lattices Obtained from Construction A 448
6. Decoding £8 448
Chapter 21
Voronoi Cells of Lattices and Quantization Errors
J.H. Conway and N.J.A. Sloane 449
1. Introduction 449
2. Second Moments of Polytopes 451
2.A Dirichlet s Integral 451
2.B Generalized Octahedron or Crosspolytope 452
2.C The H Sphere 452
2.D n Dimensional Simplices 452
2.E Regular Simplex 453
2.F Volume and Second Moment of a Polytope in Terms
of its Faces 453
2.G Truncated Octahedron 454
2.H Second Moment of Regular Polytopes 454
2.1 Regular Polygons 455
2.J Icosahedron and Dodecahedron 455
2.K The Exceptional 4 Dimensional Polytopes 455
3. Voronoi Cells and the Mean Squared Error of Lattice
Quantizers 456
3.A The Voronoi Cell of a Root Lattice 456
3..B Voronoi Cell for An 459
3.C Voronoi Cell for Dn (n s= 4) 462
3.D Voronoi Cells for £„,£„£„ 462
3.E Voronoi Cell for D*n 463
3.F Voronoi Cell for A* 472
3.G The Walls of the Voronoi Cell 474
Chapter 22
A Bound for the Covering Radius of the Leech Lattice
S.P. Norton 476
xlii Contents
Chapter 23
The Covering Radius of the Leech Lattice
J.H. Conway, R.A. Parker and N.J.A. Sloane 478
1. Introduction 478
2. The Coxeter Dynkin Diagram of a Hole 480
3. Holes Whose Diagram Contains an An Subgraph 484
4. Holes Whose Diagram Contains a Dn Subgraph 495
5. Holes Whose Diagram Contains an En Subgraph 502
Chapter 24
Twenty Three Constructions for the Leech Lattice
J.H. Conway and N.J.A. Sloane 506
1. The Holy Constructions 506
2. The Environs of a Deep Hole 510
Chapter 25
The Cellular Structure of the Leech Lattice
R.E. Borcherds, J.H. Conway and L. Queen 513
1. Introduction 513
2. Names for the Holes 513
3. The Volume Formula 514
4. The Enumeration of the Small Holes 519
Chapter 26
Lorentzian Forms for the Leech Lattice
J.H. Conway and N.J.A. Sloane 522
1. The Unimodular Lorentzian Lattices 522
2. Lorentzian Constructions for the Leech Lattice 523
Chapter 27
The Automorphism Group of the 26 Dimensional Even
Unimodular Lorentzian Lattice
J.H. Conway 527
1. Introduction 527
2. The Main Theorem 528
Chapter 28
Leech Roots and Vinberg Groups
J.H. Conway and N.J.A. Sloane 532
1. The Leech Roots 532
2. Enumeration of the Leech Roots 541
3. The Lattices I.., for n =£ 19 547
4. Vinberg s Algorithm and the Initial Batches
of Fundamental Roots 547
5. The Later Batches of Fundamental Roots 550
Contents xliii
Chapter 29
The Monster Group and its 196884 Dimensional Space
J.H. Conway 554
1. Introduction 554
2. The Golay Code % and the Parker Loop 9 556
3. The Mathieu Group M24; the Standard Automorphisms
of 9 ! 556
4. The Golay Cocode %* and the Diagonal Automorphisms ... 556
5. The Group N of Triple Maps 557
6. The Kernel K and the Homomorphism g^ g 557
7. The Structures of Various Subgroups of N 557
8. The Leech Lattice A,4 and the Group ~QX 558
9. Short Elements 559
10. The Basic Representations of N, 559
11. The Dictionary 560
12. The Algebra .^ 561
13. The Definition of the Monster Group G, and its
Finiteness 561
14. Identifying the Monster 562
Appendix 1. Computing in S 563
Appendix 2. A Construction for 9* 563
Appendix 3. Some Relations in Q, 564
Appendix 4. Constructing Representations for TV, 566
Appendix 5. Building the Group G, 567
Chapter 30
A Monster Lie Algebra?
R.E. Borcherds, J.H. Conway, L. Queen and
N.J.A. Shane 568
Bibliography 572
Supplementary Bibliography 640
Index 657
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| any_adam_object | 1 |
| author | Conway, John Horton 1937-2020 Sloane, Neil J. A. 1939- |
| author_GND | (DE-588)119529289 (DE-588)121291553 |
| author_facet | Conway, John Horton 1937-2020 Sloane, Neil J. A. 1939- |
| author_role | aut aut |
| author_sort | Conway, John Horton 1937-2020 |
| author_variant | j h c jh jhc n j a s nja njas |
| building | Verbundindex |
| bvnumber | BV008184065 |
| callnumber-first | Q - Science |
| callnumber-label | QA166 |
| callnumber-raw | QA166.7 |
| callnumber-search | QA166.7 |
| callnumber-sort | QA 3166.7 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 170 SK 380 |
| classification_tum | MAT 103f MAT 052f MAT 209f |
| ctrlnum | (OCoLC)26350679 (DE-599)BVBBV008184065 |
| dewey-full | 511/.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.6 |
| dewey-search | 511/.6 |
| dewey-sort | 3511 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Second edition |
| format | Book |
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| id | DE-604.BV008184065 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T09:18:01Z |
| institution | BVB |
| isbn | 0387979123 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005401196 |
| oclc_num | 26350679 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-384 DE-824 DE-634 DE-83 DE-11 DE-188 DE-29T DE-19 DE-BY-UBM |
| owner_facet | DE-91G DE-BY-TUM DE-384 DE-824 DE-634 DE-83 DE-11 DE-188 DE-29T DE-19 DE-BY-UBM |
| physical | XLIII, 679 Seiten Illustrationen |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer-Verlag |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spellingShingle | Conway, John Horton 1937-2020 Sloane, Neil J. A. 1939- Sphere packings, lattices and groups Grundlehren der mathematischen Wissenschaften Analise Combinatoria larpcal Groupes finis Pavage et remplissage (Géométrie combinatoire) Sphère Treillis, Théorie des Finite groups Lattice theory Sphere packings Gitter Mathematik (DE-588)4157375-4 gnd Kugelpackung (DE-588)4165929-6 gnd Quadratische Form (DE-588)4128297-8 gnd Kombinatorik (DE-588)4031824-2 gnd Gittertheorie (DE-588)4157394-8 gnd Packungsproblem (DE-588)4173057-4 gnd Klassifikation (DE-588)4030958-7 gnd Überdeckung Mathematik (DE-588)4186551-0 gnd |
| subject_GND | (DE-588)4157375-4 (DE-588)4165929-6 (DE-588)4128297-8 (DE-588)4031824-2 (DE-588)4157394-8 (DE-588)4173057-4 (DE-588)4030958-7 (DE-588)4186551-0 |
| title | Sphere packings, lattices and groups |
| title_auth | Sphere packings, lattices and groups |
| title_exact_search | Sphere packings, lattices and groups |
| title_full | Sphere packings, lattices and groups J. H. Conway, N. J. A. Sloane ; with additional contributions by E. Bannai, R.E. Borcherds, J. Leech, S.P. Norton, A.M. Odlyzko, R.A. Parker, L. Queen and B.B. Venkov |
| title_fullStr | Sphere packings, lattices and groups J. H. Conway, N. J. A. Sloane ; with additional contributions by E. Bannai, R.E. Borcherds, J. Leech, S.P. Norton, A.M. Odlyzko, R.A. Parker, L. Queen and B.B. Venkov |
| title_full_unstemmed | Sphere packings, lattices and groups J. H. Conway, N. J. A. Sloane ; with additional contributions by E. Bannai, R.E. Borcherds, J. Leech, S.P. Norton, A.M. Odlyzko, R.A. Parker, L. Queen and B.B. Venkov |
| title_short | Sphere packings, lattices and groups |
| title_sort | sphere packings lattices and groups |
| topic | Analise Combinatoria larpcal Groupes finis Pavage et remplissage (Géométrie combinatoire) Sphère Treillis, Théorie des Finite groups Lattice theory Sphere packings Gitter Mathematik (DE-588)4157375-4 gnd Kugelpackung (DE-588)4165929-6 gnd Quadratische Form (DE-588)4128297-8 gnd Kombinatorik (DE-588)4031824-2 gnd Gittertheorie (DE-588)4157394-8 gnd Packungsproblem (DE-588)4173057-4 gnd Klassifikation (DE-588)4030958-7 gnd Überdeckung Mathematik (DE-588)4186551-0 gnd |
| topic_facet | Analise Combinatoria Groupes finis Pavage et remplissage (Géométrie combinatoire) Sphère Treillis, Théorie des Finite groups Lattice theory Sphere packings Gitter Mathematik Kugelpackung Quadratische Form Kombinatorik Gittertheorie Packungsproblem Klassifikation Überdeckung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005401196&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT conwayjohnhorton spherepackingslatticesandgroups AT sloaneneilja spherepackingslatticesandgroups |
Inhaltsverzeichnis
Paper/Kapitel scannen lassen
Paper/Kapitel scannen lassen
Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 052 2001 A 10984(2)
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |