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Tuesday, January 23, 2018

**Abstract:** The field of analytic combinatorics studies the asymptotic behaviour of sequences through analytic properties of their generating functions. In addition to the now classical univariate theory, recent work in the study of analytic combinatorics in several variables (ACSV) has shown how to derive asymptotics for the coefficients of certain D-finite functions by representing them as diagonals of multivariate rational functions. We detail the rich theory of ACSV from a computer algebra viewpoint, with an eye towards automatic implementations that can be used by those with no specialized knowledge in the field. Applications from several areas of combinatorics, number theory, and physics will be discussed.

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