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A Gentle Introduction to Analytic Combinatorics in Several Variables

Lecturer: Prof. Marni Mishna

lecture no.: 326.020

ECTS: 1.50, hours: 1.0

Schedule:

Mon, 21.1., 14:30 - 16:00
Wed, 23.1., 10:15 - 11:45
Thu, 24.1., 15:30 - 17:00
Mon, 28.1., 14:30 - 16:00
Wed, 30.1., 10:15 - 11:45
Thu, 31.1., 15:30 - 17:00

All lectures take place in the RICAM seminar room S2 416-1.

Abstract: Complex analytic techniques have slowly become standard in the combinatorial enumeration toolbox. In particular,  singularity analysis of univariate functions can be used to determine asymptotic counting formulas for a huge number of classes. Techniques to handle the multivariate case are necessarily more subtle and challenging. This course will provide the necessary background to understand the basic techniques of coefficient asymptotics of rational functions. We will review univariate techniques, and then examine the methods presented in the 2013 book Analytic Combinatorics in Several Variables (or ACSV) of Pemantle and Wilson, and apply them to pedagogical, yet generalizable examples. We draw our examples from recent research in lattice path enumeration and integer points in polytopes.