Combinatorics : a problem oriented approach

✍ Scribed by Daniel A Marcus

• Publisher: Mathematical Association of America
• Year: 1998
• Tongue: English
• Leaves: 147
• Series: Classroom resource materials (Unnumbered)
• Category: Library

✦ Table of Contents

Cover......Page 1
Copyright page......Page 3
Title page......Page 4
Contents......Page 8
Preface......Page 10
PART I Basics......Page 12
Counting Strings......Page 14
Permutations......Page 16
Probability......Page 17
Rearrangements and Derangements......Page 18
Section Summary......Page 19
More Problems......Page 20
B Combinations......Page 24
Pascal’s Triangle......Page 26
Binomial Expansions......Page 28
Combinations Allowing Repeptition......Page 29
Consistently Dominated Sequences......Page 32
Section Summary......Page 34
More Problems......Page 35
C Distributions......Page 42
Distributions of Identical Objects......Page 43
Distribution Numbers......Page 45
Multinomial Expansions......Page 47
The T-Number Triangle......Page 49
Ordered Distributions: The Flagpole Problem......Page 52
Section Summary......Page 53
More Problems......Page 54
D Partitions......Page 58
The Stirling Number Triangle......Page 61
Numerical Partitions......Page 62
Numerical Partitions with Unequal Parts......Page 65
More Problems......Page 66
Stirling Numbers of the First Kind......Page 69
PART II Special Counting Methods......Page 72
E Inclusion and Exclusion......Page 74
Why Inclusion/Exclusion Works......Page 78
Elements in a Given Number of Sets......Page 80
More Problems......Page 81
F Recurrence Relations......Page 84
The Stamp Problem......Page 85
Words with Limits on Consecutive Repetitions......Page 86
Solving a Recurrence Relation......Page 89
Derangement Numbers......Page 90
More Problems......Page 92
Counting Regions......Page 95
G Generating Functions......Page 98
Synthetic Multiplication......Page 99
The Coin Problem......Page 100
Counting Words: Exponential Generating Functions......Page 101
More Problems......Page 104
Rotations of a String......Page 108
Rotations of a Cube......Page 120
More Problems......Page 122
Groups of Transformations......Page 125
List of Standard Problems......Page 130
Dependence of Problems......Page 134
Answers to Selected Problems......Page 138
Index......Page 146