دانلود کتاب Combinatorial Methods

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Cover......Page 1
Series......Page 2
Title page......Page 3
Copyright page......Page 4
PREFACE......Page 5
TABLE OF CONTENTS......Page 7
1. Set Generating Functions......Page 11
2. Numerical Generating Functions......Page 13
Fibonacci Numbers......Page 14
1. Inclusion - Exclusion Principle......Page 17
The Euler Function......Page 18
Rencontres, Derangement or Montmort Problem......Page 19
The Menage Problem......Page 20
2. Permutations with Restricted Position. The Master Theorem......Page 22
Exercises......Page 23
Example......Page 28
Rencontre Problem......Page 29
Menage Problem......Page 31
3. Extension of the Master Theorem......Page 37
a) Counting with allowed transitions......Page 41
b) Counting with prohibited transitions......Page 42
a) Distribution of unlabeled objects: Compositions......Page 44
b) Distribution of unlabeled objects: Partitions......Page 46
3. Ramsey\'s Theorem......Page 52
Example......Page 57
a) Distinguishable boxes......Page 58
b) Collections of pairs -- graph theory......Page 59
c) Indistinguishable boxes (and labeled objects)......Page 67
d) Partially labeled graphs - The Polya Theorem......Page 68
Examples......Page 71
Proof of Polya\' s Theorem......Page 72
Examples......Page 74
Exercises......Page 77
e) Counting unrooted (free) unlabeled graphs......Page 78
Dissimilarity Theorem......Page 79
Example......Page 80
A. Random Walk on Lattices......Page 81
1. Regular Cubic Lattices......Page 82
Examples......Page 83
2. General Lattices......Page 88
i) Nearest neighbor random walk on a face centered cubic lattice......Page 89
ii) Nearest neighbor random walk on a body centered cubic lattice......Page 90
1. The Ballot Problem......Page 91
Example......Page 93
2. One Dimensional Lattice Gas......Page 95
1. Counting Figures on a Lattice, General Algebraic Approach......Page 99
2. The Dimer Problem — Transfer Matrix Method......Page 101
3. The Dimer Problem -- Pfaffian Method......Page 111
4. The Dimer Problem — First Permanent Method......Page 121
5. The Dimer Problem — Second Permanent Method......Page 126
1. The Ice Problem -- Introduction......Page 133
2. Square Ice — The Transfer Matrix Method......Page 139
3. Square Ice — Exact Solution......Page 144
4. Other Hydrogen Bonded Models — Dimer Solution......Page 158
1. Introduction......Page 166
2. Estimates of the Curie Temperature......Page 168
3. Combinatorial Solution of the Ising Model......Page 179
4. Other Combinatorial Solutions......Page 187
5. Spin Correlations......Page 191
INDEX......Page 201
Series......Page 215