Combinatorial theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1986
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 440 S. |
| ISBN: | 0471091383 |
Internformat
MARC
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| 100 | 1 | |a Hall, Marshall |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Combinatorial theory |c Marshall Hall |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1986 | |
| 300 | |a XV, 440 S. | ||
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| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Analyse combinatoire | |
| 650 | 7 | |a Analyse combinatoire |2 ram | |
| 650 | 7 | |a Combinatieleer |2 gtt | |
| 650 | 4 | |a Combinatorial analysis | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
1 / PERMUTATIONS AND COMBINATIONS 1
1.1 Definitions 1
1.2 Applications to Probability 4
Problems 6
2 / INVERSION FORMULAE 8
2.1 The Principle of Inclusion and Exclusion.
Mobius Inversion 8
2.2 Partially Ordered Sets and Their Mobius Functions 15
Problems 18
3 / GENERATING FUNCTIONS AND RECURSIONS 20
3.1 Rules and Properties 20
3.2 Combinatorial Problems 24
Problems 28
4 / PARTITIONS 31
4.1 Partitions. Identities and Arithmetic Properties 31
4.2 Asymptotic Properties of p(ri) 43
Problems 46
xi
xU Contents
5 / DISTINCT REPRESENTATIVES 48
5.1 The Theorems of P. Hall and D. Konig 48
5.2 The Permanent 56
5.3 Proof of the van der Waerden Conjecture 58
5.4 Permanents of Integral Matrices with Constant
Line Sum 69
Problems 72
6 / RAMSEY S THEOREM 73
6.1 Statement of the Theorem 73
6.2 Application of Ramsey s Theorem 74
Problems 75
7 / SOME EXTREMAL PROBLEMS 77
7.1 The Assignment Problem 77
7.2 Dilworth s Theorem 81
Problems 84
8 / CONVEX SPACES AND LINEAR PROGRAMMING 85
8.1 Convex Spaces. Convex Cones and Their Duals 85
8.2 Linear Inequalities 89
8.3 Linear Programming. The Simplex Method 96
Contents xiii
9 / GRAPHICAL METHODS. DEBRUIJN SEQUENCES 110
9.1 Complete Cycles 110
9.2 Theorems on Graphs 112
9.3 Proof of the DeBruijn Theorem 114
9.4 Strongly Regular Graphs 118
9.5 Finite Permutation Groups of Rank 3 122
10 / BLOCK DESIGNS 126
10.1 General Discussion 126
10.2 Elementary Theorems on Block Designs 129
10.3 The Bruck Ryser Chowla Theorem 133
10.4 Statement of the Hasse Minkowski Theorem.
Applications 139
11 / DIFFERENCE SETS 147
11.1 Examples and Definitions 147
11.2 Finite Fields 150
11.3 The Theorem of Singer 155
11.4 The Multiplier Theorem 159
11.5 Difference Sets in General Groups 164
11.6 Some Families of Difference Sets 170
12 / FINITE GEOMETRIES 199
12.1 Foundations 199
12.2 Finite Geometries as Block Designs 203
12.3 Finite Planes 205
12.4 Some Types of Finite Planes 211
xiv Contents
13 / ORTHOGONAL LATIN SQUARES 222
13.1 Orthogonality and Orthogonal Arrays 222
13.2 Main Theorems 223
13.3 Constructions of Orthogonal Squares 228
13.4 The End of the Euler Conjecture 234
14 / HADAMARD MATRICES 238
14.1 Paley s Constructions 238
14.2 Williamson s Method 254
14.3 An Infinite Class of Williamson Matrices 257
14.4 Three Recent Methods 261
15 / GENERAL CONSTRUCTIONS OF BLOCK DESIGNS 264
15.1 Methods of Construction 264
15.2 Basic Definitions. The Hanani Theorems 264
15.3 Direct Construction Methods 271
15.4 Triple Systems 277
15.5 Block Designs with k Greater Than 3 289
15.6 Wilson s Theorem 293
15.7 Some Infinite Families of Designs 305
15.8 Biplanes 320
16 / THEOREMS ON COMPLETION AND EMBEDDING 336
16.1 Connor s Method 336
16.2 Copositive and Completely Positive Quadratic
Forms 348
16.3 Rational Completions of Incidence Matrices 359
16.4 Integral Solutions of the Incidence Equation 368
Contents xv
17 / CODING THEORY AND BLOCK DESIGNS 376
17.1 Error Correcting Codes 376
17.2 Weight Enumerators. The MacWilliams Equations 377
17.3 Applications of Codes to Designs. General Theory 381
17.4 Group Invariants. Gleason s Theorem and Its
Generalizations 386
17.5 Applications to Planes of Order 10 390
17.6 The Symmetric (41, 16, 6) Design 399
appendix I Balanced Incomplete Block Designs with from
3 to 20 Replications 405
appendix II Hadamard Matrices of the Williamson Type 424
BIBLIOGRAPHY 428
INDEX 437
|
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| dewey-sort | 3511 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV001931545 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:37:27Z |
| institution | BVB |
| isbn | 0471091383 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001259005 |
| oclc_num | 12807598 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-91 DE-BY-TUM DE-384 DE-703 DE-739 DE-20 DE-29T DE-706 DE-634 DE-83 DE-11 |
| owner_facet | DE-91G DE-BY-TUM DE-91 DE-BY-TUM DE-384 DE-703 DE-739 DE-20 DE-29T DE-706 DE-634 DE-83 DE-11 |
| physical | XV, 440 S. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Wiley |
| record_format | marc |
| spelling | Hall, Marshall Verfasser aut Combinatorial theory Marshall Hall 2. ed. New York [u.a.] Wiley 1986 XV, 440 S. txt rdacontent n rdamedia nc rdacarrier Analyse combinatoire Analyse combinatoire ram Combinatieleer gtt Combinatorial analysis Kombinatorik (DE-588)4031824-2 gnd rswk-swf Kombinatorik (DE-588)4031824-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001259005&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hall, Marshall Combinatorial theory Analyse combinatoire Analyse combinatoire ram Combinatieleer gtt Combinatorial analysis Kombinatorik (DE-588)4031824-2 gnd |
| subject_GND | (DE-588)4031824-2 |
| title | Combinatorial theory |
| title_auth | Combinatorial theory |
| title_exact_search | Combinatorial theory |
| title_full | Combinatorial theory Marshall Hall |
| title_fullStr | Combinatorial theory Marshall Hall |
| title_full_unstemmed | Combinatorial theory Marshall Hall |
| title_short | Combinatorial theory |
| title_sort | combinatorial theory |
| topic | Analyse combinatoire Analyse combinatoire ram Combinatieleer gtt Combinatorial analysis Kombinatorik (DE-588)4031824-2 gnd |
| topic_facet | Analyse combinatoire Combinatieleer Combinatorial analysis Kombinatorik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001259005&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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