AEC Summer School, 2014. Introduction to map enumeration

Here are some notes for the course, and the exercise sheet (If you were at the school, do not hesitate to ask for complements, references, or hints by email).

Here is a (corrected) version of the slides of the first lecture.

Here are some reference that can complement the course:

• Bousquet-Mélou and Jehanne, Polynomial equations with one catalytic variable, algebraic series and map enumeration.
• Flajolet and Sedgewick book (of course for its content on singularity analysis, but also for Section VII. 8.2 dedicated to the Tutte equation)
• Bender and Canfield's reference papers on enumeration of maps of genus g I and II.
• My paper with Marcus and Schaeffer on the combinatorial counting of genus g maps.

Some other complements to go further:

• Bouttier, Di Francesco and Guitter's classical paper, for the bijective enumeration of planar maps by degree.
• My paper with Féray and Fusy dealing with the enumeration of one-face maps.
• Goulden and Jackson's paper exposing the link between map enumeration and the KP hierarchy (see also here).
• A survey by Le Gall and Miermont on random maps (not covered in this course).
• Lando and Zvonkin's book for the link with algebraic geometry, and with matrix integrals (not covered in this course).