Description

Book Synopsis
Catalan numbers, named after the French-Belgian mathematician Eugène Charles Catalan (1814-1894), arise in a variety of combinatorial problems. They have many interesting properties, a rich history, and numerous arithmetic, number-theoretical, analytical and combinatorial connections, as well as a variety of classical and modern applications. Considering the long list of open problems and questions related to the classical case, its relatives (Bell numbers, Motzkin numbers, Narayana numbers, etc.) and its generalizations, this book provides a broad perspective on the theory of this class of special numbers that will be useful and of interest to both professionals and a general audience.The book begins with the history of the problem, before defining the considered numerical sets. The recurrence equation, closed formula, and generating function are then presented, followed by the simplest properties and number-theoretical properties. Later chapters discuss the relationships between Catalan numbers and other special numbers, as well as their applications and open problems.

Catalan Numbers

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    A Hardback by Elena Deza

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      Book details

      Publisher World Scientific Publishing Co Pte Ltd
      Published 1/27/2025
      ISBN-13 9789811293221
      978-9811293221
      ISBN-10 9811293228
      Also in:
      Number theory

      Description

      Book Synopsis
      Catalan numbers, named after the French-Belgian mathematician Eugène Charles Catalan (1814-1894), arise in a variety of combinatorial problems. They have many interesting properties, a rich history, and numerous arithmetic, number-theoretical, analytical and combinatorial connections, as well as a variety of classical and modern applications. Considering the long list of open problems and questions related to the classical case, its relatives (Bell numbers, Motzkin numbers, Narayana numbers, etc.) and its generalizations, this book provides a broad perspective on the theory of this class of special numbers that will be useful and of interest to both professionals and a general audience.The book begins with the history of the problem, before defining the considered numerical sets. The recurrence equation, closed formula, and generating function are then presented, followed by the simplest properties and number-theoretical properties. Later chapters discuss the relationships between Catalan numbers and other special numbers, as well as their applications and open problems.

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