By Steven Roman
This textbook presents an creation to the Catalan numbers and their outstanding houses, in addition to their a number of functions in combinatorics. Intended to be available to scholars new to the topic, the ebook starts off with extra trouble-free themes earlier than progressing to extra mathematically refined topics. Each bankruptcy makes a speciality of a selected combinatorial item counted by way of those numbers, together with paths, bushes, tilings of a staircase, null sums in Zn+1, period buildings, walls, diversifications, semiorders, and more. Exercises are incorporated on the finish of e-book, in addition to tricks and suggestions, to aid scholars receive a greater grab of the material. The textual content is perfect for undergraduate scholars learning combinatorics, yet also will entice a person with a mathematical historical past who has an curiosity in studying concerning the Catalan numbers.
“Roman does an admirable task of supplying an creation to Catalan numbers of a unique nature from the former ones. He has made a good number of issues on the way to express the flavour of Catalan combinatorics. [Readers] will gather a very good feeling for why such a lot of mathematicians are enthralled by way of the notable ubiquity and magnificence of Catalan numbers.”
- From the foreword by means of Richard Stanley
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An Introduction to Catalan Numbers (Compact Textbooks in Mathematics) by Steven Roman