Combinatorial designs and tournaments:
Gespeichert in:
| Vorheriger Titel: | Anderson, Ian Combinatorial designs |
|---|---|
| 1. Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon Press
1997
|
| Schriftenreihe: | Oxford lecture series in mathematics and its applications
6 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 237 S. graph. Darst. |
| ISBN: | 0198500297 |
Internformat
MARC
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| 490 | 1 | |a Oxford lecture series in mathematics and its applications |v 6 | |
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| 650 | 7 | |a Ensembles de différence |2 ram | |
| 650 | 7 | |a Hadamard, Matrices d' |2 ram | |
| 650 | 4 | |a Plan symétrique | |
| 650 | 7 | |a Steiner, Systèmes de |2 ram | |
| 650 | 7 | |a Tournois (théorie des graphes) |2 ram | |
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Datensatz im Suchindex
| _version_ | 1804126744928583680 |
|---|---|
| adam_text | Contents
List of abbreviations xii
1 Introduction to basics 1
1.1 Block designs 1
1.2 Resolvability U
1.3 Latin squares 15
1.4 Pairwise balanced designs 23
1.5 Systems of distinct representatives 26
1.6 Finite fields 30
1.7 Exercises 1 34
2 Difference methods 39
2.1 Difference sets 39
2.2 Difference systems 43
2.3 Difference systems for tournaments 47
2.4 Pure and mixed differences 51
2.5 Multipliers of difference sets 56
2.6 Exercises 2 58
3 Symmetric designs 62
3.1 The extreme cases 62
3.2 Hadamard designs and matrices 64
3.3 Constructing Hadamard matrices 68
3.4 Finite projective planes 76
3.5 The Bruck Chowla Ryser theorem 77
3.6 Exercises 3 79
4 Orthogonal Latin squares 83
4.1 Early results 83
4.2 Orthogonal arrays 87
4.3 Using pairwise balanced designs 91
4.4 The collapse of the Euler conjecture 93
4.5 Transversal designs 97
x Contents
4.6 Transversal designs and orthogonal arrays 100
4.7 Group divisible designs 102
4.8 Exercises 4 104
5 Self orthogonal Latin squares 108
5.1 SOLS and mixed doubles tournaments 108
5.2 New SOLS from old 111
5.3 The Brayton Coppersmith Hoffman theorem 113
5.4 Resolvable SAMDRR 116
5.5 Some examples 121
5.6 Exercises 5 123
6 Steiner systems 125
6.1 Existence of Steiner triple systems 125
6.2 Cyclic Steiner triple systems 129
6.3 Introduction to f designs 136
6.4 Steiner systems 140
6.5 Exercises 6 142
7 Kirkman triple systems 148
7.1 Early history 148
7.2 The theorem of Ray Chaudhuri, Wilson, and Lu Jiaxi 153
7.3 Sylvester s problem 156
7.4 Exercises 7 157
8 League schedules 160
8.1 Round robin tournaments 160
8.2 Venues 161
8.3 Carry over effects 164
8.4 Bipartite tournaments 165
8.5 Exercises 8 169
9 Room squares and bridge tournaments 172
9.1 Room squares 172
9.2 The use of starters 176
9.3 Triplication and quintuplication 181
9.4 Balanced Room squares for bridge tournaments 184
9.5 Exercises 9 192
Contents xi
10 Balanced tournament designs 195
10.1 Factored balanced tournament designs 195
10.2 Partitioned balanced tournament designs 202
10.3 Howell designs 204
10.4 Exercises 10 206
11 Whist tournaments 209
11.1 The use of differences 209
11.2 Using pairwise balanced designs 212
11.3 Product theorems 215
11.4 Using SAMDRR 217
11.5 Whist tournaments for 4« + 1 players 218
11.6 Directedwhist and triplewhist tournaments 221
11.7 Exercises 11 225
Bibliography 227
Index of ( v, k, A)BIBDs explicitly constructed 233
Index 235
|
| any_adam_object | 1 |
| author | Anderson, Ian 1942- |
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| callnumber-raw | QA166.25 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 890 |
| ctrlnum | (OCoLC)36037983 (DE-599)BVBBV012136232 |
| 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 |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:22:20Z |
| institution | BVB |
| isbn | 0198500297 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008219659 |
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| physical | XI, 237 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Clarendon Press |
| record_format | marc |
| series | Oxford lecture series in mathematics and its applications |
| series2 | Oxford lecture series in mathematics and its applications |
| spelling | Anderson, Ian 1942- Verfasser (DE-588)122240782 aut Combinatorial designs and tournaments Ian Anderson Oxford Clarendon Press 1997 XI, 237 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford lecture series in mathematics and its applications 6 Carré latin orthogonal Configurations et schémas combinatoires ram Ensembles de différence ram Hadamard, Matrices d' ram Plan symétrique Steiner, Systèmes de ram Tournois (théorie des graphes) ram Combinatorial designs and configurations Tournaments (Graph theory) Ablaufplanung (DE-588)4122751-7 gnd rswk-swf Turnier (DE-588)4061272-7 gnd rswk-swf Kombinatorische Designtheorie (DE-588)4164747-6 gnd rswk-swf Turnier (DE-588)4061272-7 s Ablaufplanung (DE-588)4122751-7 s Kombinatorische Designtheorie (DE-588)4164747-6 s DE-604 Früher u.d.T. Anderson, Ian Combinatorial designs Oxford lecture series in mathematics and its applications 6 (DE-604)BV009910017 6 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008219659&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Anderson, Ian 1942- Combinatorial designs and tournaments Oxford lecture series in mathematics and its applications Carré latin orthogonal Configurations et schémas combinatoires ram Ensembles de différence ram Hadamard, Matrices d' ram Plan symétrique Steiner, Systèmes de ram Tournois (théorie des graphes) ram Combinatorial designs and configurations Tournaments (Graph theory) Ablaufplanung (DE-588)4122751-7 gnd Turnier (DE-588)4061272-7 gnd Kombinatorische Designtheorie (DE-588)4164747-6 gnd |
| subject_GND | (DE-588)4122751-7 (DE-588)4061272-7 (DE-588)4164747-6 |
| title | Combinatorial designs and tournaments |
| title_auth | Combinatorial designs and tournaments |
| title_exact_search | Combinatorial designs and tournaments |
| title_full | Combinatorial designs and tournaments Ian Anderson |
| title_fullStr | Combinatorial designs and tournaments Ian Anderson |
| title_full_unstemmed | Combinatorial designs and tournaments Ian Anderson |
| title_old | Anderson, Ian Combinatorial designs |
| title_short | Combinatorial designs and tournaments |
| title_sort | combinatorial designs and tournaments |
| topic | Carré latin orthogonal Configurations et schémas combinatoires ram Ensembles de différence ram Hadamard, Matrices d' ram Plan symétrique Steiner, Systèmes de ram Tournois (théorie des graphes) ram Combinatorial designs and configurations Tournaments (Graph theory) Ablaufplanung (DE-588)4122751-7 gnd Turnier (DE-588)4061272-7 gnd Kombinatorische Designtheorie (DE-588)4164747-6 gnd |
| topic_facet | Carré latin orthogonal Configurations et schémas combinatoires Ensembles de différence Hadamard, Matrices d' Plan symétrique Steiner, Systèmes de Tournois (théorie des graphes) Combinatorial designs and configurations Tournaments (Graph theory) Ablaufplanung Turnier Kombinatorische Designtheorie |
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