This volume presents a clear and concise treatment of an increasingly important branch of mathematics. A unique introductory survey complete with easy-to-understand examples and sample problems, this text includes information on such basic combinatorial tools as recurrence relations, generating functions, incidence matrices, and the non-exclusion principle. It also provides a study of block designs, Steiner triple systems, and expanded coverage of the marriage theorem, as well as a unified account of three important constructions which are significant in coding theory
Author(s): Anderson I.
Series: Oxford Applied Mathematics and Computing Science Series
Publisher: CLARENDON PRESS
Year: 1974
Language: English
Pages: 132
Tags: Математика;Дискретная математика;Комбинаторика;
Anderson I. A First Course in Combinatorial Mathematics, OAPMCS,(CP,1974)(132p) ......Page 3
Copyright ......Page 4
Preface ......Page 5
Contents ......Page 7
1. INTRODUCTION TO BASIC IDEAS 1 ......Page 9
2.1. Permutations 8 ......Page 16
2.2. Ordered selections 9 ......Page 17
2.3. Unordered selections 11 ......Page 19
2.4. Further remarks on the binomial theorem 18 ......Page 26
2.5. Miscellaneous problems on Chapter 2. 19 ......Page 27
3.1. Pairings within a set 21 ......Page 29
3.2. Pairings between sets 24 ......Page 32
3.3. An optimal assignment problem 29 ......Page 37
3.4. Gale’s optimal assignment problem 34 ......Page 42
3.5. Further reading on Chapter 3 37 ......Page 45
4.1. Some miscellaneous problems 38 ......Page 46
4.2. Fibonacci-type relations 42 ......Page 50
4.3. Using generating functions 45 ......Page 53
4.4. Miscellaneous methods 54 ......Page 62
4.5. Counting simple electrical networks 59 ......Page 67
5.1. The principle 63 ......Page 71
5.2. Rook polynomials 67 ......Page 75
6.1. Block designs 77 ......Page 85
6.2. Square block designs 83 ......Page 91
6.3. Hadamard configurations 88 ......Page 96
6.4. Error-correcting codes 92 ......Page 100
7.1. Introductory remarks 97 ......Page 105
7.2. Steiner systems 101 ......Page 109
7.3. 5(5,8,24) 105 ......Page 113
7.4. Leech’s lattice 112 ......Page 120
SOLUTIONS TO EXERCISES 117 ......Page 125
BIBLIOGRAPHY 121 ......Page 129
INDEX 123 ......Page 131
cover......Page 1
