.

0 (hodnocen0 x )

(3) Půjčeno:3x 

BK

London : Springer, 2002

viii,200 s.

ISBN 1-85233-236-0 (brož.)

Springer undergraduate mathematics series

Obsahuje předmluvu, dodatek, rejstřík

Bibliografie: s. 195-198

Matematika diskrétní - učebnice vysokošk.

000030944

1. Counting and Binomial Coefficients 1 // 1.1 Basic Principles 1 // 1.2 Factorials 2 // 1.3 Selections 3 // 1.4 Binomial Coefficients and Pascal’s Triangle 6 // 1.5 Selections with Repetitions 10 // 1.6 A Useful Matrix Inversion 13 // 2. Recurrence 19 // 2.1 Some Examples 19 // 2.2 The Auxiliary Equation Method 23 // 2.3 Generating Functions 26 // 2.4 Derangements 28 // 2.5 Sorting Algorithms 32 // 2.6 Catalan Numbers 34 // 3. Introduction to Graphs 43 // 3.1 The Concept of a Graph 43 // 3.2 Paths in Graphs 46 // 3.3 Trees 47 // 3.4 Spanning Trees 50 // 3.5 Bipartite Graphs 52 // 3.6 Planarity 54 // 3.7 Polyhedra 60 // 4. Travelling Round a Graph 69 // 4.1 Hamiltonian Graphs 69 // 4.2 Planarity and Hamiltonian Graphs 71 // 4.3 The Travelling Salesman Problem 74 // 4.4 Gray Codes 76 // 4.5 Eulerian Graphs 78 // 4.6 Eulerian Digraphs 81 // Partitions and Colourin // 5.1 Partitions of a Set // 5.2 Stirling Numbers // 5.3 Counting Functions // 5.4 Vertex Colourings of Graphs // 5.5 Edge Colourings of Graphs // 6. The Inclusion-Exclusion Principle 107 // 6.1 The Principle 107 // 6.2 Counting Surjections 112 // 6.3 Counting Labelled Trees 113 // 6.4 Scrabble 114 // 6.5 The Ménage Problem 115 // 7. Latin Squares and Hall’s Theorem 121

// 7.1 Latin Squares and Orthogonality 121 // 7.2 Magic Squares 125 // 7.3 Systems of Distinct Representatives 127 // 7.4 From Latin Squares to Affine Planes 131 // 8. Schedules and 1-Factorisations 137 // 8.1 The Circle Method 137 // 8.2 Bipartite Tournaments and 1-Factorisations of Kn,n 142 // 8.3 Tournaments from Orthogonal Latin Squares 145 // 9. Introduction to Designs 149 // 9.1 Balanced Incomplete Block Designs 149 // 9.2 Resolvable Designs 156 // 9.3 Finite Projective Planes 159 // 9.4 Hadamard Matrices and Designs 161 // 9.5 Difference Methods 165 // 9.6 Hadamard Matrices and Codes 167 // Appendix 179 // Solutions 183 // Further Reading 195 // Bibliography 197 // Index 199