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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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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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Section 0.2 Order and Selection 11
Recurrences
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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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Reals to Integers
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Section 0.3 Rules for Counting 17
Pigeonhole Principle
Fig 0.3.3
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Evaluating Sums
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Section 0.3 Rules for Counting 19
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Empty Sums and Empty Products
Multisets
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Section 0.3 Rules for Counting 21
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0.4 COUNTING SELECTIONS
Ordered Selections
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Section 0.4 Counting Selections 23
Unordered Selections
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Selections with Repetitions
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Section 0.4 Counting Selections 25
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Fig 0.4.1
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Section 0.4 Counting Selections 27
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Distributions into Labeled Cells
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Section 0.4 Counting Selections 29
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Section 0.4 Counting Selections 33
Partitions of a Set
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0.5 PERMUTATIONS
2-Line Representation of Permutations
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Section 0.5 Permutations 37
Fig 0.5.2
Cyclic Permutations
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Fig 0.5.3
Fig 0.5.4
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Section 0.5 Permutations 39
Disjoint Cycle Representation
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Section 0.5 Permutations 41
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Section 0.5 Permutations 43
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Section 0.5 Permutations 45
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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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0.7 NUMERIC OPERATIONS
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Section 0.7 Numeric Operations 51
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0.8 COMBINATORIAL DESIGNS
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Section 0.8 Combinatorial Designs 53
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Fig 0.8.1