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.In the combinatorics volume, the IMO combinatorics problems are organized into six chapters: "Enumerative Combinatorics Problems," "Existence Problems," "Extremal Combinatorial Problems," "Operation and Logical Reasoning Problems," "Combinatorial Geometry Problems," and "Graph Theory Problems." Each chapter begins with an introduction to the relevant foundational knowledge and methods, followed by a reclassification and reorganization of past IMO problems. Multiple elegant solutions are provided for some of the problems, along with a statistical analysis of their difficulty.The book concludes with a record of past IMO participation and award information, as well as an index of combinatorics problems, facilitating further study and convenient reference. This series is suitable for researchers in mathematical competitions, mathematics educators, and contestants.