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 #Dn), 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.