Fibonacci and Catalan numbers. An introduction (Q2881042)

This book has grown out of courses given by the author over the last twenty years on Fibonacci and Catalan numbers. The audience for the book is primarily undergraduates, and most of the material may be accessible already for high school students. The book also provides historical overviews, exercises, bibliographies and a variety of examples that are useful to more advanced university students.NEWLINENEWLINEThe first part of the book (Chapters 1--17) treats the Fibonacci and Lucas numbers in detail, shows their basic properties and looks at their appearance in different branches of mathematics and other sciences, such as compositions (with restrictions on their parts), palindromes, arrangement of chess pieces on chess boards, tilings, optics, botany, computer science, graph theory, contiguous arrangements of circles in the plane, and many more. The proofs of the properties are tailored to the audience, and are often outlined and based on inductive arguments, combinatorial bijections and explicit calculations (Binet formula).NEWLINENEWLINEThe second part of the book (Chapters 18--36) deals with the many aspects of Catalan numbers, namely, as they can be found in the count of balanced strings, Dyck paths, Young tableaux, triangulations of polygons, noncrossing increasing trees, orders, topological sorting, maximal cliques, sporting events, pattern avoidance in permutations, noncrossing partitions, handshaking problem and many more. The final chapters then give some properties of the related Narayana, Motzkin, Fine and Schröder numbers as well as the generalized Catalan numbers. Over 50 pages are dedicated to the solution of the odd-numbered exercises that are given in this well-rounded text. An Instructor's Solution Manual can be obtained from the publisher. It contains also the solution of the even-numbered exercises.