Combinatorial Enumeration

Fall 2004, MATH 5819
School of Mathematics and Statistics, Carleton University


Instructor: Daniel Panario
Office: #4372 HP, Tel: (613) 520 2600 (Ext. 2159)
Email: daniel@math.carleton.ca
Lectures: Tuesdays and Thursdays 2:30 - 4:00. Room: HP 4369
Office hours: Tuesdays and Thursdays 2:05- 2:25 and 4:05 - 4:30, or by appointment (send me mail or talk to me).


Current announcements

This space will be used for announcements. Check it regularly.


General Information

This course covers basic fundamental counting techniques for combinatorics. The first part of the course deals with ordinary and exponential generating functions and their applications to permutations, partitions, rooted trees, etc. We also focus on multivariate generating functions and computation of moments. Then, we give an introduction to hypergeometric functions and the Wilf-Zeilberger method. The cycle index of the symmetric group is also presented. The rest of the course is centered around asymptotics. We briefly comment on real asymptotics, Lagrange inversion formula and singularity analysis of generating functions. If time allows, we finish with an introduction to a selected topic from one of the following areas: random graphs, random combinatorial structures, hypergeometric functions.


Textbooks

There is no textbook for the course.

We will use Herb Wilf 's Generatingfunctionology (you can download it for free!).

We will also use material from the coming book:

Some chapters of this book are available as technical reports at Philippe Flajolet's webpage. In particular, we will extensively use the first two issues of the book:

Other texts for consult:

Lectures per month


Contact Information:

Office Hours: Tuesdays and Thursdays 4:10 - 5:00.
e-mail: daniel@math.carleton.ca