Syllabus
Formal power series. Lagrange inversion formula.
Ordinary and exponential generating functions, and the combinatorial interpretation of their basic operations. Overview of basic theory of complex analytic functions.
Rational and meromorphic functions, the residue theorem. Applications of complex analysis to the enumeration of combinatorial objects.
Multivariate generating functions, and their application to the study of random combinatorial objects.
Annotation
The course will focus on solving combinatorial problems by application of generating functions, with emphasis on methods based on complex analysis. No previous knowledge of complex analysis is necessary, but basic knowledge of generating functions is expected.