Combinatorial Enumeration

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Transcript of Combinatorial Enumeration

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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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    4 Chapter 0 Introductory Survey

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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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    8 Chapter 0 Introductory Survey

    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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    14 Chapter 0 Introductory Survey

    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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    30 Chapter 0 Introductory Survey

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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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    48 Chapter 0 Introductory Survey

    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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    54 Chapter 0 Introductory Survey

    Fig 0.8.1