Discrete mathematics using latin squares:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Wiley
1998
|
| Series: | A Wiley interscience publication
Wiley-interscience series in discrete mathematics and optimization |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 305 S. graph. Darst. |
| ISBN: | 0471240648 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface xiii
PART I. LATIN SQUARES
1 A Brief Introduction to Latin Squares 3
1.1 Introduction 3
1.2 How Many Latin Squares Are There? 3
1.3 Orthogonal Squares 5
1.4 Statistical Applications 9
1.5 Codes 11
1.6 Tournament Designs 12
1.7 Geometry 13
1.8 Completing Partial Latin Squares 14
1.9 Exercises 15
1.10 Notes 16
References 17
2 Mutually Orthogonal Latin Squares 18
2.1 Introduction 18
2.2 Prime Powers 20
2.3 Nonprime Powers 22
2.4 Miscellaneous Results 32
2.5 Exercises 34
2.6 Notes 36
References 39
PART II. GENERALIZATIONS
3 Orthogonal Hypercubes 43
3.1 Introduction 43
3.2 Orthogonal Sets of Hypercubes 45
3.3 Construction of Complete Sets 47
3.4 Recursive Construction 51
vjj
viii Contents
3.5 MacNeish Construction 57
3.6 Exercises 60
3.7 Notes 61
References 62
4 Frequency Squares 63
4.1 Introduction 63
4.2 Mutually Orthogonal Frequency Squares 63
4.3 Exercises 69
4.4 Notes 70
References 70
PART III. RELATED MATHEMATICS
5 Principle of Inclusion Exclusion 75
5.1 Second Row of a Latin Square 75
5.2 Rook Polynomials 80
5.3 Third Row of a Latin Square 86
5.4 Exercises 91
5.5 Notes 93
References 93
6 Groups and Latin Squares 94
6.1 Introduction 94
6.2 Groups and Latin Squares 95
6.3 Row Latin Squares 97
6.4 Sets of Orthogonal Latin Squares 98
6.5 Maximal Order in RLn 101
6.6 Exercises 103
6.7 Notes 104
References 104
7 Graphs and Latin Squares 106
7.1 Graph Theory Basics 106
7.2 Latin Squares and Bipartite Graphs 106
7.3 Latin Squares and Complete Graph Factorizations 110
7.4 Row Complete Latin Squares and Paths in Graphs 115
7.5 Strongly Regular Graphs 121
7.6 Orthogonal Latin Square Graphs 123
7.7 Exercises 126
7.8 Notes 127
References 128
Contents ix
PART IV. APPLICATIONS
8 Affine and Projective Planes 131
8.1 Basic Properties 131
8.2 Algebraic Derivation 133
8.3 Planes and MOLS 136
8.4 Projective Planes 138
8.5 Desarguesian Planes 143
8.6 Nondesarguesian Planes 146
8.7 Exercises 150
8.8 Notes 151
References 152
9 Orthogonal Hypercubes and Affine Designs 153
9.1 Designs 153
9.2 Hypercubes and Designs 158
9.3 Hypercubes and Affine Geometries 161
9.4 MOFS and Designs 166
9.5 Exercises 171
9.6 Notes 172
References 173
10 Magic Squares 175
10.1 Introduction 175
10.2 Diagonal Latin Squares 176
10.3 Other Magic Objects 179
10.4 Exercises 180
10.5 Notes 181
References 181
11 Room Squares 182
11.1 Introduction 182
11.2 Room Square Construction 183
11.3 Exercises 186
11.4 Notes 186
References 186
12 Statistics 188
12.1 Introduction 188
12.2 Analysis of Variance 188
12.3 Latin Square Designs 189
12.4 Designs with More Than Three Variables 197
x Contents
12.5 Exercises 201
12.6 Notes 204
References 204
13 Error Correcting Codes 205
13.1 Introduction to Coding Theory 205
13.2 Basics of Error Correcting Codes 205
13.3 Codes from MOLS 209
13.4 More Optimal Codes 213
13.5 Maximal Codes and Latin Square Enumeration 221
13.6 Exercises 224
13.7 Notes 225
References 226
14 Cryptology 228
14.1 Introduction 228
14.2 Encryption 228
14.3 Secret Sharing Schemes 230
14.4 Discrete Logarithms 234
14.5 Exercises 238
14.6 Notes 239
References 239
15 (t, m, s) Nets 241
15.1 Introduction 241
15.2 Nets 242
15.3 Nets and MOLS 244
15.4 Higher Orthogonality 250
15.5 Exercises 252
15.6 Notes 253
References 254
16 Miscellaneous Applications of Latin Squares 255
16.1 Introduction 255
16.2 Mutually Orthogonal Partial Latin Squares and Applications 255
16.3 Conflict Free Access to Parallel Memories 258
16.4 Broadcast Squares 259
16.5 Tournaments 260
16.6 Other Applications 263
16.7 Notes 264
References 265
Contents xi
APPENDIXES
A Algebraic Background 269
A.I A Few Basics of Number Theory and Abstract Algebra 269
A.2 Vector Spaces 274
A.3 Exercises 277
A.4 Notes 278
References 278
B Hints and Partial Solutions to Selected Exercises 279
Author Index 297
Subject Index 301
|
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| id | DE-604.BV012359796 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:26:11Z |
| institution | BVB |
| isbn | 0471240648 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008380767 |
| oclc_num | 38180103 |
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| owner | DE-384 DE-29T DE-188 |
| owner_facet | DE-384 DE-29T DE-188 |
| physical | XV, 305 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Wiley |
| record_format | marc |
| series2 | A Wiley interscience publication Wiley-interscience series in discrete mathematics and optimization |
| spelling | Laywine, Charles F. Verfasser aut Discrete mathematics using latin squares Charles F. Laywine ; Gary L. Mullen New York u.a. Wiley 1998 XV, 305 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Wiley interscience publication Wiley-interscience series in discrete mathematics and optimization Numerieke wiskunde gtt Magic squares Lateinisches Quadrat (DE-588)4166852-2 gnd rswk-swf Diskrete Mathematik (DE-588)4129143-8 gnd rswk-swf Lateinisches Quadrat (DE-588)4166852-2 s DE-604 Diskrete Mathematik (DE-588)4129143-8 s Mullen, Gary L. 1947- Verfasser (DE-588)123964059 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008380767&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Laywine, Charles F. Mullen, Gary L. 1947- Discrete mathematics using latin squares Numerieke wiskunde gtt Magic squares Lateinisches Quadrat (DE-588)4166852-2 gnd Diskrete Mathematik (DE-588)4129143-8 gnd |
| subject_GND | (DE-588)4166852-2 (DE-588)4129143-8 |
| title | Discrete mathematics using latin squares |
| title_auth | Discrete mathematics using latin squares |
| title_exact_search | Discrete mathematics using latin squares |
| title_full | Discrete mathematics using latin squares Charles F. Laywine ; Gary L. Mullen |
| title_fullStr | Discrete mathematics using latin squares Charles F. Laywine ; Gary L. Mullen |
| title_full_unstemmed | Discrete mathematics using latin squares Charles F. Laywine ; Gary L. Mullen |
| title_short | Discrete mathematics using latin squares |
| title_sort | discrete mathematics using latin squares |
| topic | Numerieke wiskunde gtt Magic squares Lateinisches Quadrat (DE-588)4166852-2 gnd Diskrete Mathematik (DE-588)4129143-8 gnd |
| topic_facet | Numerieke wiskunde Magic squares Lateinisches Quadrat Diskrete Mathematik |
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