Combinatorial problems in mathematical competitions (Mathematical Olympiad)

This book focuses on combinatorial problems in mathematical competitions. It provides basic knowledge on how to solve combinatorial problems in mathematical competitions, and also introduces important solutions to combinatorial problems and some typical problems with often-used solutions. Some enlightening and novel examples and exercises are well chosen in this book. With this book, readers can explore, analyze and summarize the ideas and methods of solving combinatorial problems. Their mathematical culture and ability will be improved remarkably after reading this book. Pt. 1. Fundamental knowledge. ch. 1. Principles and formulas of counting. ch. 2. Pigeonhole principle and mean value principle. ch. 3. The generating functions. ch. 4. Recurrence sequence of numbers -- pt. 2. Basic method. ch. 5. Classification and method of fractional steps. ch. 6. Correspondent method. ch. 7. Counting in two ways. ch. 8. Recurrence method. ch. 9. Coloring method and evaluation method. ch. 10. Reduction to absurdity and the extreme principle. ch. 11. Local adjustment method. ch. 12. Construction method -- pt. 3. Typical problems. ch. 13. Combinatiorial counting problems. ch. 14. Existence problems and the proofs of inequalities in combinatorial problems. ch. 15. Combinatorial extremum problems Principles And Formulas Of Counting -- Pigeonhole Principles And Mean Value Principles -- Generating Functions -- Recurrence Sequence Of Numbers -- Classification And Method Of Fractional Steps -- Corresponding Method -- Counting In Two Ways -- Recurrence Method -- Coloring Method And Evaluation Method -- Reduction Of Absurdity And The Extreme Principle -- Local Adjusted Method -- Constructive Method -- Combinatorial Counting Problems -- Existence Problems And The Proof Of Inequalities In Combinatorial Problems -- Combinatorial Extremum Problems. Yao Zhang. Focuses on combinatorial problems in mathematical competitions. This work provides basic knowledge on how to solve combinatorial problems in mathematical competitions, and also introduces solutions to combinatorial problems and some typical problems with often-used solutions.