Welcome to Week 5 of "Analytic Combinatorics." This week, we study one of the jewels of analytic combinatorics: the Flajolet-Odlyzko theorem that provides universal laws giving coefficient asymptotics for the large class of GFs having singularities of the square-root and logarithmic type. ---------- Lecture 6: Singularity Analysis. This lecture addresses the basic Flajolet-Odlyzko theorem, where we find the domain of analyticity of the function near its dominant singularity, approximate using functions from standard scale, and then transfer to coefficient asymptotics term-by-term. Lecture 7: Applications of Singularity Analysis. We see how the Flajolet-Odlyzko approach leads to universal laws covering combinatorial classes built with the set, multiset, and recursive sequence constructions. Then we consider applications to many of the classic combinatorial classes that we encountered in Lectures 1 and 2. ---------- Your assignment for this week, due at 11:59PM on Thursday, April 21, 2022 is to write up and submit solutions to Web Exercises VI.1, VI.2, and VII.1 on the "Analytic Combinatorics" booksite. As usual, submit a potential exam question on the week's material. Submit files named "AC5-Q1.pdf" "AC5-Q2.pdf" "AC5-Q3.pdf" "AC5-QQ.pdf" RS