Effective Analytic Combinatorics in Several Variables.

Stephen Melczer, SFU

Tuesday May 23rd at 1:30pm in K9509.

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.