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In this chapter, we examine some of the most important classes of labelled objects, including surjections, set partitions, permutations, as well as labelled graphs, trees, and mappings from a finite set into itself. Certain aspects of words can also be treated by this theory, a fact which has important consequences not only in combinatorics itself but also in probability and statistics. | ANALYTIC COMBINATORICS PART TWO http ac.cs.princeton.edu 2. Labelled structures and EGFs Analytic combinatorics overview A. SYMBOLIC METHOD 1. OGFs 2. EGFs 3. MGFs B. COMPLEX ASYMPTOTICS 4. Rational Meromorphic 5. Applications of R M 6. Singularity Analysis 7. Applications of SA 8. Saddle point specification SYMBOLIC METHOD GF equation COMPLEX ASYMPTOTICS asymptotic estimate T desired result 2 Attention Much of this lecture is a quick review of material in Analytic Combinatorics Part I One consequence it is a bit longer than usual To Students who took Analytic Combinatorics Part I Bored because you understand it all GREAT Skip to the section on labelled trees and do the exercises. To Students starting with Analytic Combinatorics Part II Moving too fast Want to see details and motivating applications No problem watch Lectures 5 7 and 9 in Part .
