RISC AEC Summer School 2018

This is the website for the course An Invitation to Analytic Combinatorics in Several Variables at the 2018 RISC AEC Summer School.

The main reference for the course is my PhD thesis (especially the pedagogical Chapters 1, 3, 4, 5, 6, and 9).

Analytic Combinatorics in Several Variables: Effective Asymptotics and Lattice Path Enumeration
S. Melczer. PhD Thesis, University of Waterloo and ENS Lyon, 2017.
https://arxiv.org/abs/1709.05051

Notes and Worksheets

A scan of notes from the first class is available here.
A scan of notes from the second class is available here.
A scan of notes from the third class is available here.
The Sage iPython notebook from the third class (best to have a recent version of Sage) is available here.
A scan of notes from the fourth class is available here.
The Mathematica worksheet from the exercise class is here (you need the RISCErgoSum Mathematica package - see here).
A scan of notes from the final class is available here.
The Maple package demoed in the final class can be found here.
The small amount of electronic slides from all classes can be found here.

Exercise Sheets

The first exercise sheet is here.
The second exercise sheet is here.

Additional References

The in-class lectures will be self-contained, however additional details can be found in the following sources.

Analytic Combinatorics
P. Flajolet and B. Sedgewick. Cambridge University Press, 2009.
http://ac.cs.princeton.edu/home/

Analytic Combinatorics in Several Variables
R. Pemantle and M. Wilson. Cambridge University Press, 2013.
https://www.math.upenn.edu/~pemantle/papers/ACSV.pdf

Generatingfunctionology
H. Wilf. Academic Press, 1990.
https://www.math.upenn.edu/~wilf/DownldGF.html

Algorithmes Efficaces en Calcul Formel [Efficient Algorithms in Computer Science]
A. Bostan, F. Chyzak, M. Giusti, R. Lebreton, G. Lecerf, B. Salvy and E. Schost, 2017.
https://hal.archives-ouvertes.fr/AECF/
(In French)