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Record Nr. |
UNINA9911019679703321 |
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Autore |
Merris Russell <1943-> |
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Titolo |
Combinatorics / / Russell Merris |
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Pubbl/distr/stampa |
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Hoboken, N.J., : John Wiley, c2003 |
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ISBN |
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9786610366200 |
9781280366208 |
1280366206 |
9780470342879 |
0470342870 |
9780471458494 |
047145849X |
9780471449683 |
0471449687 |
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Edizione |
[2nd ed.] |
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Descrizione fisica |
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1 online resource (572 p.) |
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Collana |
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Wiley-Interscience series in discrete mathematics and optimization |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references (p. 501-502) and indexes. |
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Nota di contenuto |
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Combinatorics Second Edition; Contents; Preface; Chapter 1 The Mathematics of Choice; 1.1. The Fundamental Counting Principle; 1.2. Pascal's Triangle; *1.3. Elementary Probability; *1.4. Error-Correcting Codes; 1.5. Combinatorial Identities; 1.6. Four Ways to Choose; 1.7. The Binomial and Multinomial Theorems; 1.8. Partitions; 1.9. Elementary Symmetric Functions; *1.10. Combinatorial Algorithms; Chapter 2 The Combinatorics of Finite Functions; 2.1. Stirling Numbers of the Second Kind; 2.2. Bells, Balls, and Urns; 2.3. The Principle of Inclusion and Exclusion; 2.4. Disjoint Cycles |
2.5. Stirling Numbers of the First KindChapter 3 Pólya's Theory of Enumeration; 3.1. Function Composition; 3.2. Permutation Groups; 3.3. Burnside's Lemma; 3.4. Symmetry Groups; 3.5. Color Patterns; 3.6. Pólya's Theorem; 3.7. The Cycle Index Polynomial; Chapter 4 Generating Functions; 4.1. Difference Sequences; 4.2. Ordinary Generating Functions; 4.3. Applications of Generating Functions; 4.4. |
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Exponential Generating Functions; 4.5. Recursive Techniques; Chapter 5 Enumeration in Graphs; 5.1. The Pigeonhole Principle; *5.2. Edge Colorings and Ramsey Theory; 5.3. Chromatic Polynomials |
*5.4. Planar Graphs5.5. Matching Polynomials; 5.6. Oriented Graphs; 5.7. Graphic Partitions; Chapter 6 Codes and Designs; 6.1. Linear Codes; 6.2. Decoding Algorithms; 6.3. Latin Squares; 6.4. Balanced Incomplete Block Designs; Appendix A1 Symmetric Polynomials; Appendix A2 Sorting Algorithms; Appendix A3 Matrix Theory; Bibliography; Hints and Answers to Selected Odd-Numbered Exercises; Index of Notation; Index |
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Sommario/riassunto |
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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 styleTimely and appropriate examplesNumerous well-chosen exercisesFlex |
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