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Marcus D.A. — Combinatorics: A Problem Oriented Approach
Marcus D.A. — Combinatorics: A Problem Oriented Approach

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Название: Combinatorics: A Problem Oriented Approach

Автор: Marcus D.A.

Аннотация:

This book teaches the art of enumeration, or counting, by leading the reader through a series of carefully chosen problems that are arranged strategically to introduce concepts in a logical order and in a provocative way. It is organized in eight sections, the first four of which cover the basic combinatorial entities of strings, combinations, distributions, and partitions. The last four cover the special counting methods of inclusion and exclusion, recurrence relations, generating functions, and the methods of Pуlya and Redfield that can be characterized as "counting modulo symmetry." The unique format combines features of a traditional textbook with those of a problem book. The subject matter is presented through a series of approximately 250 problems, with connecting text where appropriate, and is supplemented by approximately 200 additional problems for homework assignments. Many applications to probability are included throughout the book. While intended primarily for use as the text for a college-level course taken by mathematics, computer science, and engineering students, the book is suitable as well for a general education course at a good liberal arts college, or for self study.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 156

Добавлена в каталог: 11.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Binary system      3
Binomial expansion      17
Birthday problem      10 11
Bit      3
Bit string      9 18
Bumside, W.      111
cards      10 25 44 45 66 81
Chessboard      9
Circular arrangement      9 26 58 59 102 104 112
Coin flipping      10 24
Coin problem      89
Combination      13 14 23
Combination allowing repetition      18—21 23
Combination lock      9
Combination number      14—16 23
Combination with limited repetition      67 87
Consecutive repetition      6 18 75
Consistently dominated sequence      21
Counting paths      22 23
Counting regions      84
Cycle code      107 108 111
Cycle index polynomial      107 108 111
Cycle polynomial      107 108
Derangement      7 8 11
Derangement number      8 64 71 74 79—81
distribution      31 32 35 42
Distribution into identical boxes      52
Distribution number      34 42
Distribution of identical objects      32—34 42
Distribution of type $(m_1, ..., m_n)$      35 48
Divisibility      11 28 49 64 71 72
Election problem      27
Exponential generating function      90—93
Fibonacci sequence      74 79 81 83
Flagpole problem with distinct poles      41 43
Flagpole problem with identical poles      57
Generating function      87 88 93
Group of transformations      107 108 114 115
Inclusion and exclusion      66 67 70 87
Invariant number of a reflection      104
Invariant number of a rotation      101 111
key ring      9
Length of a combination      14
Length of a string      4 8
Length of an orbit      97
Linear recurrence relation      79 81
Lottery      25
Multinomial coefficient      35
Multinomial expansion      36 37
Numerical partition      51.55.90
Numerical partition numbers      52—55 90
Numerical partition with unequal parts      54
Orbit      97 111
Ordered distribution      41 43
Partition number triangle      52 56 57
Partition of a set      47 55 85
Partition of type $(m_1, ..., m_n)$      48 55
Pascal’s triangle      15 16 23 24 27 40
Pattern inventory      105 106 108 111
Permutation      5
Poker hand      25
Polya — Redfield method      97
Polya, George      110
Prime numbers      11 28 71
probability      6—8
Product rule      5 8
Radio station names      9
Rearrangement      7 8 16 34 36
Recurrence relation      73 81
Redfield, J.H.      110
Reflection      103
Rotation group      99
Rotation of a cube      109
Rotation of a dodecahedron      117
Rotation of a square      98 103
Rotation of a string      97 111
Rotation of a tetrahedron      116
Rotational orbit      101
Solving a recurrence relation      78 79 83
Stabilizer group      100
Stabilizer number      100
Stamp problem      74 81
Stirling number triangle      50 56
Stirling numbers of the first kind      58 59
Stirling numbers of the second kind      49 55
String      3 8
subsets      9 16 72 83
Synthetic multiplication      88 93
System of recurrence relations      77
T-number triangle      38 39 50
T-numbers      38—40 43 49 50 66 70 95
Tree diagram      76 77
Union of sets      63 64 70
Word      3
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