Math 68. Algebraic Combinatorics

Fall 2007

·        Instructor:         Sergi Elizalde

·        Lectures:           TuTh 10:00-11:50 in 201 Kemeny

·        X-period:           W 3:00-3:50

·        Office Hours:    Tu 11:50-12:30, Th 1:30-3:30, and by appointment

·        Office:               332 Kemeny

·        Email:               

·        Phone:               646-8191

Course description

This is an introductory course in algebraic and enumerative combinatorics. You will learn how to apply techniques from algebra to solve enumeration problems, and to use combinatorial methods to solve questions arising in other areas of mathematics. No prior knowledge of combinatorics is expected, but some familiarity with linear algebra and finite groups is preferable.


·       Problem Set 1, due on 10/11/07.

·       Problem Set 2, due on 10/25/07.

·       Problem Set 3, due on 11/8/07.

·       Problem Set 4, due on 11/27/07.

The final exam will be handed out on Thursday, November 29, and due on Tuesday, December 4.

Recommended texts

There is no textbook required for this course.

Most of the material in the course will be taken from these three sources:

- [Aig] Martin Aigner, A Course in Enumeration, Graduate Texts in Mathematics 238, Springer, 2007.

- [dM] Anna de Mier, Lecture notes for "Enumerative Combinatorics". [Download]

- [St] Richard P. Stanley, Topics in algebraic combinatorics, course notes, preliminary version. I will hand out these notes in class.

Other useful books that you can look at are:

- [EC1] [EC2] Richard P. Stanley, Enumerative Combinatorics, Vols. I and II, Cambridge University Press, 1997/1999.

- [Wf] Herb Wilf, Generatingfunctionology, Academic Press, 1990. Also available online at

- [vLW] J.H. van Lint, R.M. Wilson, A course in Combinatorics, Cambridge University Press, Cambridge, 1992.

- [Bo] Miklos Bóna, A walk through combinatorics, World Scientific, 2002.

- [FS] P. Flajolet, R. Sedgewick, Analytic Combinatorics. The preliminary version of this forthcoming book is available online at

- [Bg] Kenneth P. Bogart, Enumerative Combinatorics Through Guided Discovery. It is available at

- [BS] A. Björner, R. Stanley, A Combinatorial Miscellany [Download].


Here is a tentative list of the topics that will be covered, together with the corresponding references. The main references for each topic are in bold.

Homework, exams, and grading

The course grade will be based on

The homework will consist of a problem set every two weeks. Collaboration is permitted, but you are not allowed to copy someone else's work. The solutions must be written individually. You have to mention on your problem set the names of the students that you worked with, and also which books or articles you used.

The final will be a take-home exam. You must work on the problems on your own. No collaboration permitted in the exam.

Class participation involves attending lectures, as well as asking and answering questions in class.

The final project will consist of preparing a topic and presenting it in class. Students should work in groups of 2 or 3. Here are possible topics for the project.

Students with disabilities: Students with disabilities enrolled in this course that may need disability-related classroom accommodations are encouraged to make an office appointment to see me before the end of the second week of the term. All discussions will remain confidential, although the Student Accessibility Services office may be consulted to discuss appropriate implementation of any accommodation requested.

Last modified on Nov 12, 2007.