Contents 1. Counting and Binomial Coefficients 1.1 Basic Principles 1.2 Factorials 1.3 Selections 1.4 Binomial Coefficients and Pascal's Triangle 1.5 Selections with- --Repetitions 1.6 AUsefulMatrixInversion 2. Recurrence 2.1 Some Examples 2.2 The Auxiliary Equation Method 2.3 Generating Fhnctions 2.4 Derangements 2.5 Sorting Algorithms 2.6 Catalan Numbers 3. Introduction to Graphs 3.1 The Concept of a Graph 3.2 Paths in Graphs 3.3 Trees 3.4 Spanning Trees 3.5 Bipartite Graphs 3.t5 Planarity 3.7 Polyhedra. 4. Travelling Round a Graph 4 1 Hamiltonian Graphs 4.2 Planarity and Hamiltonian Graphs 4.3 The Travelling Salesman Problem 4.4 Gray Codes 4.5 EulerianDigraphs 5. Partitions and Colourings 5.1 Partitions of a Set 5.2 StirlingNumbers 5.3 Counting Functions 5.4 Vertex Colourings of Graphs 5.5 Edge Colourings of Graphs 6 The Inclusion-Exclusion Principle 6.1 The Principle 6.2 Counting Surjections 6.3 Counting Labelled Trees 6.4 Scrabble. 15.5 The MSnage Problem 7. Latin Squares and Hall's Theorem. 7.1 Latin-Squares and -Orthogonality 7.2 Magic Squares 7.3 Systems of Distinct Representatives 7.4 From Latin Squares to Affine Planes 8 Schedules and 1-Factorisations 8.1 The Circle Method 8.2 Bipartite Tournaments and 1-Factorisations of Kn 8.3 Tournaments from Orthogonal Latin Squares 9. Introduction to Designs. 9.1 Balanced Incomplete Block Designs 0.2 Resolvable Designs 0.3 Finite Projective Planes 0.4 Hadamard Matrices and Designs 0.15 Difference Methods 9.15 Hadamard Matrices and Codes Appendix Solutions Further Reading Bibliography Index
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