## CO 430/630 Algebraic Combinatorial Enumeration

### Fall 2006

### MWF 12:30 - 1:30

### MC 4064

(Topics will include the following, perhaps among others.)
### I. The Lagrange Implicit Function Theorem

### II. Exponential Generating Functions

### III. Introduction to Symmetric Functions

### IV. Enumeration and Representations of *sl(2,C)*

### V. Enumerative Combinatorics of Electrical Networks

### Grading

Homework: 15%

Midterm Exam: 30%

Final Exam: 55%

Graduate (630) students will be expected to do more (and more difficult)
work than undergraduate (430) students.

### Tutorials and Office Hours

There are none of either! Instead, as this is a small class of seniors and
graduate students, my office is open to you anytime. (Uh... any time I'm
there. ;-)
Come in and chat... if I'm busy we can arrange another time.

My contact information:

office: MC 5040

phone: (519) 888-4567 x2487

e-mail:
` dgwagner@math.uwaterloo.ca `

### Assignments, Solutions, and Notes

Homework assignments and solutions, Midterm Exam solutions, and
Course Notes will be posted here as the semester progresses.

Formal Power Series, and the Lagrange Implicit Function Theorem (LIFT).
[ PDF file ]

Exponential Generating Functions I and II, and LIFT again.
[ PDF file ]

HOMEWORK ASSIGNMENT #1: due Monday, October 9. *edit* Wednesday, October 11.

CO 430: Exercises 7.5, 7.8(a), 11.5 (part (b) asks for
#*D*_{n}), 11.6, 11.9, 11.12, 12.1.

CO 630: All the above plus Exercises 7.8(b), 7.12, 11.15, and

(*) Show that composition of natural classes is associative (modulo
natural equivalence). That is, for natural classes *A*, *B*,
and *C*, there is a natural equivalence of classes
*A*[*B*[*C*]] == (*A*[*B*])[*C*].

HOMEWORK (MINI-)ASSIGNMENT #2: due Friday, Octber 27.

[TYPO: in Ex.12.4, h(3)=3.]

CO 430: Exercises (12.4 or 12.6) and (13.1).

CO 630: Exercises 12.4, 12.6, 13.1.

Introduction to Symmetric Functions
[ PDF file ]

HOMEWORK ASSIGNMENT #3: due Wednesday, November 15.

***edit* Friday, Nov.17th.**
[ PDF file ]

Representations of sl(2,C) and Enumeration.
[ PDF file ]

HOMEWORK ASSIGNMENT #4: due Monday, December 4.
[ PDF file ]

**FINAL EXAMINATION:** Friday, December 15.

MC 4040, 2:00 - 5:00.