Combinatorics: A Problem-Based Approach

Description

This text provides a theoretical background for several topics in combinatorial mathematics, such as enumerative combinatorics (including partitions and Burnside's lemma), magic and Latin squares, graph theory, extremal combinatorics, mathematical games and elementary probability. A number of examples are given with explanations while the book also provides more than 300 exercises of different levels of difficulty that are arranged at the end of each chapter, and more than 130 additional challenging problems, including problems from mathematical olympiads. Solutions or hints to all exercises and problems are included. The book can be used by secondary school students preparing for mathematical competitions, by their instructors, and by undergraduate students. The book may also be useful for graduate students and for researchers that apply combinatorial methods in different areas. Front Matter ....Pages I-X Introduction (Pavle Mladenović)....Pages 1-8 Arrangements, Permutations, and Combinations (Pavle Mladenović)....Pages 9-34 Binomial and Multinomial Theorems (Pavle Mladenović)....Pages 35-48 Inclusion-Exclusion Principle (Pavle Mladenović)....Pages 49-62 Generating Functions (Pavle Mladenović)....Pages 63-74 Partitions (Pavle Mladenović)....Pages 75-90 Burnside’s Lemma (Pavle Mladenović)....Pages 91-106 Graph Theory: Part 1 (Pavle Mladenović)....Pages 107-125 Graph Theory: Part 2 (Pavle Mladenović)....Pages 127-140 Existence of Combinatorial Configurations (Pavle Mladenović)....Pages 141-164 Mathematical Games (Pavle Mladenović)....Pages 165-176 Elementary Probability (Pavle Mladenović)....Pages 177-197 Additional Problems (Pavle Mladenović)....Pages 199-219 Solutions (Pavle Mladenović)....Pages 221-358 Back Matter ....Pages 359-365