Combinatorics Through Guided Discovery, 2004a

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Combinatorics Through Guided Discovery Kenneth P. Bogart Dartmouth College Editors Mitchel T. Keller Washington & Lee University Oscar Levin University of Northern Colorado Kent E. Morrison American Institute of Mathematics
Edition: First PreTeXt Edition Website: http://bogart.openmathbooks.org/ © 2004 (main text); 2017 (Preface to PreTeXt Edition) Kenneth P. Bogart (main text); Mitchel T. Keller, Oscar Levin, Kent E. Morrison (Preface to PreTeXt Edition) Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front- Cover Texts, and no Back-Cover Texts. A copy of the license is included in the appendix entitled “GNU Free Documentation License”.
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Page 7 and 8: vi a great deal of time to helping
Page 9 and 10: viii because they use an important
Page 11 and 12: x you happen to get a hard problem
Page 13 and 14: xii Discovery had been placed on th
Page 15 and 16: xiv Contents 2.3.1 Undirected graph
Page 17 and 18: xvi Contents C Exponential Generati
Page 19 and 20: 2 1. What is Combinatorics? learned
Page 21 and 22: 4 1. What is Combinatorics? For exa
Page 23 and 24: 6 1. What is Combinatorics? and the
Page 25 and 26: 8 1. What is Combinatorics? + Probl
Page 27 and 28: 10 1. What is Combinatorics? If we
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Page 31 and 32: 14 1. What is Combinatorics? k =0 1
Page 33 and 34: 16 1. What is Combinatorics? • Pr
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Page 37 and 38: 20 1. What is Combinatorics? a Prov
Page 39 and 40: 22 1. What is Combinatorics? (c) Fi
Page 41 and 42: 24 1. What is Combinatorics? (vii)
Page 43 and 44: 26 1. What is Combinatorics? · Pro
Page 45 and 46: 28 1. What is Combinatorics? 1.4 Su
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Page 49 and 50: 32 2. Applications of Induction and
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36 2. Applications of Induction and
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52 3. Distribution Problems problem
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54 3. Distribution Problems bĳecti
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56 3. Distribution Problems 3.1.3 M
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58 3. Distribution Problems broken
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60 3. Distribution Problems 3.2.2 S
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62 3. Distribution Problems coeffic
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64 3. Distribution Problems Problem
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66 3. Distribution Problems Problem
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68 3. Distribution Problems number
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70 3. Distribution Problems ⇒ Pro
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72 3. Distribution Problems ⇒ 12.
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74 4. Generating Functions • Prob
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78 4. Generating Functions x k in t
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84 4. Generating Functions the gene
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86 4. Generating Functions ◦ Prob
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88 4. Generating Functions Writing
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90 4. Generating Functions 4.4 Supp
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92 4. Generating Functions
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94 5. The Principle of Inclusion an
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100 5. The Principle of Inclusion a
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102 5. The Principle of Inclusion a
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104 6. Groups acting on sets on. We
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106 6. Groups acting on sets still
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108 6. Groups acting on sets Let us
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110 6. Groups acting on sets Proble
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112 6. Groups acting on sets 6.1.7
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114 6. Groups acting on sets ⇒ ·
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116 6. Groups acting on sets • Pr
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118 6. Groups acting on sets 3, and
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122 6. Groups acting on sets Taking
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126 6. Groups acting on sets of dif
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130 6. Groups acting on sets ⇒ Pr
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132 6. Groups acting on sets (c) Wr
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134 A. Relations Problem 329. Here
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136 A. Relations Problem 333. Draw
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138 A. Relations Problem 340. Expla
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140 A. Relations • If R is a rela
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142 A. Relations Problem 355. Suppo
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144 A. Relations
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146 B. Mathematical Induction (e) P
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148 B. Mathematical Induction shows
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150 B. Mathematical Induction cent
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152 C. Exponential Generating Funct
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170 D. Hints to Selected Problems 1
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178 D. Hints to Selected Problems t
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180 D. Hints to Selected Problems t
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184 D. Hints to Selected Problems A
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192 D. Hints to Selected Problems
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194 E. GNU Free Documentation Licen
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200 Index equivalent, 112 cycle ind
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202 Index pair structure, 159 pair,
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