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This book provides a comprehensive overview of combinatorics, which is a branch of mathematics concerning the study of finite or countable discrete structures. Combinatorial problems arise in many areas of pure mathematics such as in algebra, probability theory, topology, and geometry. Combinatorics has many applications in optimization, computer science, ergodic theory and statistical physics. Read about the aspects of combinatorics including counting the structures of a given kind and size, deciding when certain criteria can be met, constructing and analyzing objects meeting the criteria, and much more.
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