Imo Problems, Theorems, And Methods: Combinatorics

The problems in the International Mathematical Olympiad (IMO) are not only novel and interesting but also deeply rooted in profound mathematical context. The team at the International Mathematical Olympiad Research Center at East China Normal University has compiled and studied problems from past IMOs, dividing them into four volumes based on the mathematical fields involved: algebra, geometry, number theory, and combinatorics.The Combinatorics volume primarily divides IMO problems into six chapters: 'Enumerative Combinatorics Problems', 'Existence Problems', ' Extremal Combinatorial Problems', 'Operations and Logical Reasoning Problems', 'Combinatorial Geometry Problems', and 'Graph Theory Problems'. This volume begins with an explanation of the origin and development of the IMO, covering aspects such as participating teams, contestants, awards, and problems, and it then outlines the characteristics and trends of IMO combinatorial problems. Each chapter introduces relevant foundational knowledge and methods, provides some typical examples, and then classifies the IMO problems in that chapter according to the knowledge, methods, and characteristics involved. The problems are arranged in chronological order, with multiple good solutions provided for some problems, along with statistical analysis of the problem difficulty and a discussion of the Chinese team's performance.At the end of the book, there is information about past IMO participants and medal winners, as well as an index of combinatorics problems, making it convenient for readers to reference and conduct further research.