A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory

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World Scientific, 2002 - Mathematics - 406 pages
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This is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of exercises, ranging in difficulty from "routine" to "worthy of independent publication, " is included. In each section, there are also exercises that contain material not explicitly discussed in the text before, so as to provide instructors with extra choices if they want to shift the emphasis of their course.

It goes without saying that the text covers the classic areas, i.e. combinatorial choice problems and graph theory. What is unusual, for an undergraduate textbook, is that the author has included a number of more elaborate concepts, such as Ramsey theory, the probabilistic method and -- probably the first of its kind -- pattern avoidance. While the reader can only skim the surface of these areas, the author believes that they are interesting enough to catch the attention of some students. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.

 

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Contents

IV
1
V
3
VI
10
VII
11
VIII
12
IX
19
X
25
XI
26
LIII
196
LIV
200
LVI
207
LVII
214
LVIII
218
LIX
221
LX
226
LXI
229

XII
28
XIII
29
XIV
37
XV
40
XVI
43
XVII
47
XVIII
51
XIX
52
XX
65
XXI
70
XXII
73
XXIII
75
XXIV
78
XXV
79
XXVI
89
XXVII
91
XXVIII
94
XXIX
100
XXX
102
XXXI
103
XXXII
109
XXXIII
110
XXXIV
116
XXXV
120
XXXVI
123
XXXVIII
131
XXXIX
134
XL
138
XLI
139
XLII
140
XLIII
145
XLIV
160
XLV
168
XLVI
169
XLVII
171
XLVIII
183
XLIX
184
L
188
LI
190
LII
193
LXII
230
LXIII
239
LXIV
241
LXV
246
LXVI
252
LXVII
254
LXVIII
258
LXIX
259
LXX
260
LXXI
265
LXXII
268
LXXIII
275
LXXIV
278
LXXVI
279
LXXVII
283
LXXVIII
289
LXXIX
292
LXXX
293
LXXXI
295
LXXXII
296
LXXXIII
301
LXXXIV
313
LXXXV
324
LXXXVI
326
LXXXVII
327
LXXXVIII
339
LXXXIX
343
XC
345
XCI
358
XCII
361
XCIII
362
XCIV
369
XCV
374
XCVI
383
XCVII
390
XCVIII
392
XCIX
393
C
401
CI
403
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