ABSTRACT
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2.1 Introduction This chapter should have really been written by Philippe Flajolet (1948-2011), who could not make it this time. He coined the name analytic combinatorics. The present author knew Flajolet since 1979 and followed all the developments closely since then, also being a coauthor on various occasions. Flajolet and his followers started out in analysis of algorithms, a subject founded by Knuth in his series of books The art of computer programming; it became clear over the years that many techniques from classical mathematics had to be unearthed and many new ones had to be discovered. Flajolet was a pioneer in this direction; Doron Zeilberger called him a combinatorialist who became an analyst, and it was his understanding that combinatorics should have an analytic component, like number theory has analytic number theory. Flajolet, apart from being an exceptional problem solver, had a strong desire to be clear and systematic. Eventually, with coauthor Robert Sedgewick, after many years of preparations, the book Analytic Combinatorics [24] was published. It has 810 pages, and only a fraction of it can be represented here.
