**Class meets:** Tuesday and Thursday, 1-2:30 pm,
room 4-153

**Instructor:**
Alexander Postnikov

**Office hour:** Thursday, 4-5 pm

**Grader:**
Pavlo Pylyavskyy

**Description:**

Combinatorial problems and methods for their solution. Prior experience
with abstraction and proofs is helpful. Enumeration, generating
functions, recurrence relations, construction of bijections. Introduction
to graph theory.

**Course Level:** Undergraduate

**Recommended textbooks:**

*****
*Introductory Combinatorics*, R. Brualdi,
3rd or 4th edition, Prentice Hall.

*****
*A Walk through Combinatorics,* M. Bona,
World Scientific, 2002.

**Further Reading:**

*****
*Enumerative Combinatorics*, Vol 1 and Vol 2, by R. P. Stanley,
Cambridge University Press, 1996 and 1999.

**Grading:** 3 quizes 25% each, problem sets 25%, + bonuses.

**Problem Sets:**
Due every second Thursday.

- Problem Set 1 (due 09/23/2004): PostScript and PDF
- Problem Set 2 (due 10/07/2004): PostScript and PDF
- Problem Set 3 (due 10/21/2004): PostScript and PDF
- Problem Set 4 (due 11/09/2004): PostScript and PDF
- Problem Set 5 (due 12/09/2004): PostScript and PDF

**Exams:**

- Practice problems for Exam 1: PostScript and PDF
- Exam 1 (10/07/2004): PostScript and PDF
- Practice problems for Exam 2: PDF (problems from last year)
- Exam 2 (11/04/2004): PostScript and PDF
- Practice problems for Exam 3: PostScript and PDF

**Bonuses:** You can get a grading bonus if you
(a) write an article in combinatorics;
(b) invent a new interesting integer sequence and
publish it in Sloan's Encyclopedia;
(c) find a new interpretation of the Catalan numbers
that is not listed in Stanley's EC2 and Catalan Addendum;
(d) solve some of the optional bonus problems in problem sets;
or (e) solve some of the problems from the following list of

**7 open problems:**
PostScript and PDF

**Useful links:**

- Neil Sloan's on-line Encyclopedia of Integer Sequences
- Richard Stanley's EC page that includes a list of problems on Catalan numbers (PS and PDF) together with Catalan Addendum (PS and PDF)

**Lectures:** (tentative schedule)

- R 09/09/2004. Course overview. Introduction.
- T 09/14/2004. Pigeonhole principle.
- R 09/16/2004. Mathematical induction.
- T 09/21/2004. Permutations.
- R 09/23/2004. Permutations (cont'd). PS1 is due.
- T 09/28/2004. Binomial theorem.
- R 09/30/2004. Compositions.
- T 10/05/2004. Partitions.
- R 10/07/2004. Quiz I. PS2 is due.
- T 10/12/2004. Inclusion-exclusion.
- R 10/14/2004. Inclusion-exclusion (cont'd). Mobius inversion.
- T 10/19/2004. Recurrence relations.
- R 10/21/2004. Generating functions. PS3 is due.
- T 10/26/2004. Exponential generating functions.
- R 10/28/2004. Catalan numbers.
- T 11/02/2004. No class
- R 11/04/2004. Quiz II.
- T 11/09/2004. Matchings. Eulerian walks. Hamiltionian cycles.
PS4 is due.
R 11/11/2004. No class: Veterans Day

- T 11/16/2004. Trees. Counting trees.
- R 11/18/2004. Matrix-tree theorem.
- T 11/23/2004. Matrix-tree theorem (cont'd).
R 11/25/2004. No class: Thanksgiving

- T 11/20/2004. Chromatic numbers. Planar graphs.
- R 12/02/2004. Quiz III.
- T 12/07/2004. Polya counting.
- R 12/09/2004. Probabilistic method. PS5 is due.