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Chapter 0Introductory Survey

0.1 Objectives of Combinatorics0.2 Ordering and Selection

0.3 Some Rules for Counting

0.4 Counting Selections

0.5 Permutations

0.6 Graphs0.7 Number-Theoretic Operations

0.8 Combinatorial Designs

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Section 0.1 Objectives 3

0.1 OBJECTIVES

Combinatorial Enumeration

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Section 0.1 Objectives 5

Incidence Structures

Fig 0.1.1

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6 Chapter 0 Introductory Survey

Fig 0.1.2

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Section 0.1 Objectives 7

Optimization

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0.2 ORDER AND SELECTION

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Section 0.2 Order and Selection 9

Sequences and Generating Functions

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10 Chapter 0 Introductory Survey

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Section 0.2 Order and Selection 11

Recurrences

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12 Chapter 0 Introductory Survey

Combination Coef cients

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Section 0.3 Rules for Counting 13

0.3 RULES FOR COUNTING

Rules of Sum and Product

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Rule of Quotient

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Section 0.3 Rules for Counting 15

Fig 0.3.1

Fig 0.3.2

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16 Chapter 0 Introductory Survey

Reals to Integers

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Section 0.3 Rules for Counting 17

Pigeonhole Principle

Fig 0.3.3

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18 Chapter 0 Introductory Survey

Evaluating Sums

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Section 0.3 Rules for Counting 19

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20 Chapter 0 Introductory Survey

Empty Sums and Empty Products

Multisets

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Section 0.3 Rules for Counting 21

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22 Chapter 0 Introductory Survey

0.4 COUNTING SELECTIONS

Ordered Selections

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Section 0.4 Counting Selections 23

Unordered Selections

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24 Chapter 0 Introductory Survey

Selections with Repetitions

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Section 0.4 Counting Selections 25

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26 Chapter 0 Introductory Survey

Fig 0.4.1

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Section 0.4 Counting Selections 27

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28 Chapter 0 Introductory Survey

Distributions into Labeled Cells

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Section 0.4 Counting Selections 29

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32 Chapter 0 Introductory Survey

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Section 0.4 Counting Selections 33

Partitions of a Set

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34 Chapter 0 Introductory Survey

0.5 PERMUTATIONS

2-Line Representation of Permutations

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36 Chapter 0 Introductory Survey

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Section 0.5 Permutations 37

Fig 0.5.2

Cyclic Permutations

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38 Chapter 0 Introductory Survey

Fig 0.5.3

Fig 0.5.4

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Section 0.5 Permutations 39

Disjoint Cycle Representation

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40 Chapter 0 Introductory Survey

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Section 0.5 Permutations 41

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42 Chapter 0 Introductory Survey

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Section 0.5 Permutations 43

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44 Chapter 0 Introductory Survey

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Section 0.5 Permutations 45

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46 Chapter 0 Introductory Survey

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Section 0.6 Graphs 47

0.6 GRAPHS

Fig 0.6.1

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Simple and General Graphs

Degree of a Vertex

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Section 0.6 Graphs 49

Fig 0.6.2

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50 Chapter 0 Introductory Survey

0.7 NUMERIC OPERATIONS

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Section 0.7 Numeric Operations 51

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52 Chapter 0 Introductory Survey

0.8 COMBINATORIAL DESIGNS

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Section 0.8 Combinatorial Designs 53

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Fig 0.8.1