Table Of Content

Cover page Page: i Halftitle page Page: i Series page Page: ii Title page Page: ix Copyright page Page: x Contents Page: xi List of illustrations Page: xiii List of tables Page: xvii 1 What is combinatorics? Page: 1 2 Four types of problem Page: 7 Existence problems Page: 8 Construction problems Page: 14 Enumeration problems Page: 15 Optimization problems Page: 22 The efficiency of algorithms Page: 24 3 Permutations and combinations Page: 28 Ordered selections Page: 29 Unordered selections Page: 35 Distributions Page: 45 Winning the lottery Page: 47 4 A combinatorial zoo Page: 50 The box principle Page: 50 Inclusion and exclusion Page: 52 Derangements Page: 55 The Tower of Hanoi Page: 58 Poetry, pavings, and rabbits Page: 60 Job assignments and marriage Page: 63 Generators and enumerators Page: 66 The game of Scrabble Page: 67 Counting chessboards Page: 68 5 Tilings and polyhedra Page: 72 Tilings Page: 73 Polyhedra Page: 79 6 Graphs Page: 86 What is a graph? Page: 86 Trees Page: 90 Eulerian and Hamiltonian graphs Page: 93 Planar graphs Page: 99 The missing region Page: 105 The four-colour theorem Page: 106 7 Square arrays Page: 109 Magic squares Page: 110 Latin squares Page: 113 Orthogonal latin squares Page: 117 8 Designs and geometry Page: 123 Block designs Page: 124 Triple systems Page: 127 Finite projective planes Page: 129 Tying things together Page: 134 9 Partitions Page: 140 Enter Euler Page: 141 Enter Hardy and Ramanujan Page: 146 Further reading Page: 151 Index Page: 153 Social media Page: 158

Description:

How many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal's triangle? (it was not Pascal) Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. In this Very Short Introduction Robin Wilson gives an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to colour a map with different colours for neighbouring countries. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.