TY - BOOK ID - 8360272 TI - An Introduction to Catalan Numbers PY - 2015 SN - 3319221434 3319221442 PB - Cham : Springer International Publishing : Imprint: Birkhäuser, DB - UniCat KW - Algebra KW - Mathematics KW - Physical Sciences & Mathematics KW - Mathematics. KW - Computer science KW - Sequences (Mathematics). KW - Computer mathematics. KW - Combinatorics. KW - Graph theory. KW - Graph Theory. KW - Sequences, Series, Summability. KW - Mathematical Applications in Computer Science. KW - Discrete Mathematics in Computer Science. KW - Computational complexity. KW - Complexity, Computational KW - Electronic data processing KW - Machine theory KW - Combinatorics KW - Mathematical analysis KW - Mathematical sequences KW - Numerical sequences KW - Catalan numbers (Mathematics) KW - Computer science—Mathematics. KW - Computer mathematics KW - Graph theory KW - Graphs, Theory of KW - Theory of graphs KW - Combinatorial analysis KW - Topology KW - Extremal problems UR - https://www.unicat.be/uniCat?func=search&query=sysid:8360272 AB - This textbook provides an introduction to the Catalan numbers and their remarkable properties, along with their various applications in combinatorics. Intended to be accessible to students new to the subject, the book begins with more elementary topics before progressing to more mathematically sophisticated topics. Each chapter focuses on a specific combinatorial object counted by these numbers, including paths, trees, tilings of a staircase, null sums in Zn+1, interval structures, partitions, permutations, semiorders, and more. Exercises are included at the end of book, along with hints and solutions, to help students obtain a better grasp of the material. The text is ideal for undergraduate students studying combinatorics, but will also appeal to anyone with a mathematical background who has an interest in learning about the Catalan numbers. “Roman does an admirable job of providing an introduction to Catalan numbers of a different nature from the previous ones. He has made an excellent choice of topics in order to convey the flavor of Catalan combinatorics. [Readers] will acquire a good feeling for why so many mathematicians are enthralled by the remarkable ubiquity and elegance of Catalan numbers.” - From the foreword by Richard Stanley. ER -