Book contents
- Frontmatter
- Contents
- Preface to the first edition
- Preface to the second edition
- 1 Graphs
- 2 Trees
- 3 Colorings of graphs and Ramsey's theorem
- 4 Turán's theorem and extremal graphs
- 5 Systems of distinct representatives
- 6 Dilworth's theorem and extremal set theory
- 7 Flows in networks
- 8 De Bruijn sequences
- 9 Two (0, 1, ⋆) problems: addressing for graphs and a hash-coding scheme
- 10 The principle of inclusion and exclusion; inversion formulae
- 11 Permanents
- 12 The Van der Waerden conjecture
- 13 Elementary counting; Stirling numbers
- 14 Recursions and generating functions
- 15 Partitions
- 16 (0, 1)-Matrices
- 17 Latin squares
- 18 Hadamard matrices, Reed–Muller codes
- 19 Designs
- 20 Codes and designs
- 21 Strongly regular graphs and partial geometries
- 22 Orthogonal Latin squares
- 23 Projective and combinatorial geometries
- 24 Gaussian numbers and q-analogues
- 25 Lattices and Möbius inversion
- 26 Combinatorial designs and projective geometries
- 27 Difference sets and automorphisms
- 28 Difference sets and the group ring
- 29 Codes and symmetric designs
- 30 Association schemes
- 31 (More) algebraic techniques in graph theory
- 32 Graph connectivity
- 33 Planarity and coloring
- 34 Whitney Duality
- 35 Embeddings of graphs on surfaces
- 36 Electrical networks and squared squares
- 37 Pólya theory of counting
- 38 Baranyai's theorem
- Appendix 1 Hints and comments on problems
- Appendix 2 Formal power series
- Name Index
- Subject Index
Preface to the first edition
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface to the first edition
- Preface to the second edition
- 1 Graphs
- 2 Trees
- 3 Colorings of graphs and Ramsey's theorem
- 4 Turán's theorem and extremal graphs
- 5 Systems of distinct representatives
- 6 Dilworth's theorem and extremal set theory
- 7 Flows in networks
- 8 De Bruijn sequences
- 9 Two (0, 1, ⋆) problems: addressing for graphs and a hash-coding scheme
- 10 The principle of inclusion and exclusion; inversion formulae
- 11 Permanents
- 12 The Van der Waerden conjecture
- 13 Elementary counting; Stirling numbers
- 14 Recursions and generating functions
- 15 Partitions
- 16 (0, 1)-Matrices
- 17 Latin squares
- 18 Hadamard matrices, Reed–Muller codes
- 19 Designs
- 20 Codes and designs
- 21 Strongly regular graphs and partial geometries
- 22 Orthogonal Latin squares
- 23 Projective and combinatorial geometries
- 24 Gaussian numbers and q-analogues
- 25 Lattices and Möbius inversion
- 26 Combinatorial designs and projective geometries
- 27 Difference sets and automorphisms
- 28 Difference sets and the group ring
- 29 Codes and symmetric designs
- 30 Association schemes
- 31 (More) algebraic techniques in graph theory
- 32 Graph connectivity
- 33 Planarity and coloring
- 34 Whitney Duality
- 35 Embeddings of graphs on surfaces
- 36 Electrical networks and squared squares
- 37 Pólya theory of counting
- 38 Baranyai's theorem
- Appendix 1 Hints and comments on problems
- Appendix 2 Formal power series
- Name Index
- Subject Index
Summary
One of the most popular upper level mathematics courses taught at Caltech for very many years was H. J. Ryser's course Combinatorial Analysis, Math 121. One of Ryser's main goals was to show elegance and simplicity. Furthermore, in this course that he taught so well, he sought to demonstrate coherence of the subject of combinatorics. We dedicate this book to the memory of Herb Ryser, our friend whom we admired and from whom we learned much.
Work on the present book was started during the academic year 1988–89 when the two authors taught the course Math 121 together. Our aim was not only to continue in the style of Ryser by showing many links between areas of combinatorics that seem unrelated, but also to try to more-or-less survey the subject. We had in mind that after a course like this, students who subsequently attend a conference on “Combinatorics” would hear no talks where they are completely lost because of unfamiliarity with the topic. Well, at least they should have heard many of the words before. We strongly believe that a student studying combinatorics should see as many of its branches as possible.
Of course, none of the chapters could possibly give a complete treatment of the subject indicated in their titles. Instead, we cover some highlights—but we insist on doing something substantial or nontrivial with each topic. It is our opinion that a good way to learn combinatorics is to see subjects repeated at intervals.
- Type
- Chapter
- Information
- A Course in Combinatorics , pp. xi - xiiPublisher: Cambridge University PressPrint publication year: 2001