An Introduction to Catalan Numbers

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Focusing on the Catalan numbers, this textbook introduces their unique properties and applications in combinatorics. It is designed for students with varying levels of experience, starting with elementary concepts and advancing to more complex topics. Each chapter highlights a specific combinatorial object associated with Catalan numbers, such as paths, trees, staircase tilings, and null sums in Z, making it a comprehensive resource for understanding this important mathematical concept.