Analytic Combinatorics teaches a calculus that enables precise quantitative predictions of large combinatorial structures. This course introduces the symbolic method to derive functional relations among ordinary, exponential, and multivariate generating functions, and methods in complex analysis for deriving accurate asymptotics from the GF equations.

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Labelled Structures and EGFs

This lecture introduces labelled objects, where the atoms that we use to build objects are distinguishable. We use exponential generating functions EGFs to study combinatorial classes built from labelled objects. As in Lecture 1, we define combinatorial constructions that lead to EGF equations, and consider numerous examples from classical combinatorics.