The Unity of Combinatorics: Connections and Wonders

An account of how a great Guy and his Brown coauthor created a 300-page book entitled "The Unity of Combinatorics" out of a 30-page paper from 1995 of the same name. The latter was an outline of a proposed lecture series, whose purpose was to feature the many connections within the vast area of combinatorics, thereby dispelling the then prevalent notion that combinatorics is just a bag of tricks. In writing the book, we took this notion and ran with it --- and how!

I'll talk about a number of these connections and some topics that seem almost magical, including Beatty sequences, Conway worms, games played with turtles instead of coins, and a way of viewing the non-negative integers as a field. The book begins with a child playing with colored blocks on his living-room rug and ends with a description of the Miracle Octad Generator. Finally, I'll talk about working with this gentlemanly giant of the world of numbers and sequences and patterns and games.