Combinatorics
著者
書誌事項
Combinatorics
(Wiley-Interscience series in discrete mathematics and optimization)
John Wiley, c2003
2nd ed
大学図書館所蔵 全12件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
"Wiley-Interscience"--T.p.
Includes bibliographical references and indexes
内容説明・目次
内容説明
A mathematical gem-freshly cleaned and polished This book is intended to be used as the text for a first course in combinatorics. the text has been shaped by two goals, namely, to make complex mathematics accessible to students with a wide range of abilities, interests, and motivations; and to create a pedagogical tool, useful to the broad spectrum of instructors who bring a variety of perspectives and expectations to such a course.
Features retained from the first edition:
Lively and engaging writing style
Timely and appropriate examples
Numerous well-chosen exercises
Flexible modular format
Optional sections and appendices
Highlights of Second Edition enhancements:
Smoothed and polished exposition, with a sharpened focus on key ideas
Expanded discussion of linear codes
New optional section on algorithms
Greatly expanded hints and answers section
Many new exercises and examples
目次
Preface ix
Chapter 1 The Mathematics of Choice 1
1.1. The Fundamental Counting Principle 2
1.2. Pascal's Triangle 10
* 1.3. Elementary Probability 21
* 1.4. Error-Correcting Codes 33
1.5. Combinatorial Identities 43
1.6. Four Ways to Choose 56
1.7. The Binomial and Multinomial Theorems 66
1.8. Partitions 76
1.9. Elementary Symmetric Functions 87
* 1.10. Combinatorial Algorithms 100
Chapter 2 The Combinatorics of Finite Functions 117
2.1. Stirling Numbers of the Second Kind 117
2.2. Bells, Balls, and Urns 128
2.3. The Principle of Inclusion and Exclusion 140
2.4. Disjoint Cycles 152
2.5. Stirling Numbers of the First Kind 161
Chapter 3 Polya's Theory of Enumeration 175
3.1. Function Composition 175
3.2. Permutation Groups 184
3.3. Burnside's Lemma 194
3.4. Symmetry Groups 206
3.5. Color Patterns 218
3.6. Polya's Theorem 228
3.7. The Cycle Index Polynomial 241
Chapter 4 Generating Functions 253
4.1. Difference Sequences 253
4.2. Ordinary Generating Functions 268
4.3. Applications of Generating Functions 284
4.4. Exponential Generating Functions 301
4.5. Recursive Techniques 320
Chapter 5 Enumeration in Graphs 337
5.1. The Pigeonhole Principle 338
* 5.2. Edge Colorings and Ramsey Theory 347
5.3. Chromatic Polynomials 357
* 5.4. Planar Graphs 372
5.5. Matching Polynomials 383
5.6. Oriented Graphs 394
5.7. Graphic Partitions 408
Chapter 6 Codes and Designs 421
6.1. Linear Codes 422
6.2. Decoding Algorithms 432
6.3. Latin Squares 447
6.4. Balanced Incomplete Block Designs 461
Appendix A1 Symmetric Polynomials 477
Appendix A2 Sorting Algorithms 485
Appendix A3 Matrix Theory 495
Bibliography 501
Hints and Answers to Selected Odd-Numbered Exercises 503
Index of Notation 541
Index 547
「Nielsen BookData」 より