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A. Slomson — An Introduction to Combinatorics
A. Slomson — An Introduction to Combinatorics

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Название: An Introduction to Combinatorics

Автор: A. Slomson


The growth in digital devices, which require discrete formulation of problems, has revitalized the role of combinatorics, making it indispensable to computer science. Furthermore, the challenges of new technologies have led to its use in industrial processes, communications systems, electrical networks, organic chemical identification, coding theory, economics, and more. With a unique approach, Introduction to Combinatorics builds a foundation for problem-solving in any of these fields. Although combinatorics deals with finite collections of discrete objects, and as such differs from continuous mathematics, the two areas do interact. The author, therefore, does not hesitate to use methods drawn from continuous mathematics, and in fact shows readers the relevance of abstract, pure mathematics to real-world problems. The author has structured his chapters around concrete problems, and as he illustrates the solutions, the underlying theory emerges. His focus is on counting problems, beginning with the very straightforward and ending with the complicated problem of counting the number of different graphs with a given number of vertices.Its clear, accessible style and detailed solutions to many of the exercises, from routine to challenging, provided at the end of the book make Introduction to Combinatorics ideal for self-study as well as for structured coursework.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 270

Добавлена в каталог: 04.04.2020

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Предметный указатель
Abelian      119
Abstract groups      117
Anagram      28
Associativity      116
Asymptotic      44
Automorphism of a graph      155
Axioms for group actions      139
binomial      8
Binomial coefficient      7
Binomial theorem      7
Birthdays, coincidence of      18
Boole, George      99
Brackets      101
Cauchy's theorem      148
Cayley table      117
Cayley, Arthur      117
Centre of a group      148
Chessboard      136
Codomain      xiii
Combination      6
Commutative      119
composition      114
Conjugacy class      143
Conjugation      141
Coset      168
Counting problems      xii
Cycle notation      111
Cycle type      133
Degree of a vertex      153
Derangement      28
Difference equations      98
Disjoint cycle form      111
Domain      xiii
Domination      45
Dot diagram      32
Dual of a partition      33
EDGE      150
Equating coefficients, method of      61
Euler's identity      70
Fibonacci numbers      85
fix      159
Formal power series      60
formulas      36
Generated subgroup      131
Generating function      62
Goldbach's conjecture      30
Graph      150
Graph, simple      151
Group actions      139
groups      116
Groups of permutations      113
Hardy — Ramanujan formula      73
Hardy, G.H.      76
Homogeneous linear recurrence relations      86
Homomorphism      139
Identity element of a group      116
identity map      114
Inclusion-exclusion theorem      21
Index of a subgroup      128
Infinite order      129
Inhomogeneous linear recurrence relations      93
Initial condition      82
Inverse element      116
Isometry      120
Isomorphism of graphs      152
Labelled graphs      153
Labelling of a graph      155
Lagrange's theorem      128
Latin square      118
Legitimate bracket sequence      101
Listen with mother      xiv
Method of equating coefficients      61
Multinomial theorem      11
Multiplication of choices principle      3
Multiplication table      117
Node      150
Open University      xv
Orbit      143
Orbit-stabilizer theorem      145
Order of a group      125
Order of group elements      129
Ordered partition      32
Over riffle shuffle      109
Partial fractions      104
Particular solution      97
Partition      29
Pascal's triangle      9
Permutation      3 110
Poker hands      17
Polynomial function      38
Powers of group elements      129
Principle of multiplication of choices      3
probability      12
Ramanujan, S.R.A.      77
Rank      13
Rational function      104
Recurrence relation      80
Recursive definition      82
Riffle shuffle      109
Sampling with replacement      23
Simple graph      151
Stabilizer      144
Stirling's formula      47
Subgroups      123 124
Suit      13
Suit distribution      24
Symmetry      120
Symmetry groups      120
Towers of Hanoi      100
Under riffle shuffle      109
Unrestricted partition numbers      29
Vector spaces      92
Vertex      150
Void suit      13
Wallis' formula      53
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