Introduction to Combinatorics
Math 4160

I have determined the grades for the final and the course. I will not be posting them anywhere, you will need to e-mail me if you would like to know what they are before they are released. If you would like to look at your exam you will most likely find me in my office on Tuesday and Thursday during the months of May and June although it will be best to e-mail me to make an appointment to make sure that I will be there.
The final exam is listed as due April 18, 2003. I recently found out that the university offices are closed that day (my guess is that there are no finals scheduled either). If you would like to hand in the exam that day slip it under my door in S615 or give it to me if I am there. Otherwise hand it in on Monday either to N520 or my office in S615.
On the final there is one mistake I have found so far. The sum in test 1 problem number 13 should be from l=0 to n-k and not from l=0 to n. Your proof should uncover this error. Also it must be that 1 <= r <= k. The grad student version seems to be OK.
I will have office hours Monday April 7, 2003 from 1-3pm and Tuesday April 15, 2003 from 12pm-2pm.
(3/31/03) The final exam will be take-home. I will try to have it ready by Friday morning (the last day of class) and I will give you the chance to discuss it before you have two weeks to work on the exam (it should take 3 hours). I will be available to answer questions for at least a few hours the week before the exam is due.
Problem number 1 and 2 of homework 5 in the Burnside's theorem and Polya enumeration section have to do with the symmetries of the cube. This really isn't hard if you look carefully at something like a die or a block. You do not need to write down a single permutation, just the cycle structure. I have written a few hints to get you started.
The midterm exams will be on Friday, January 31 and Friday, March 7
The homework assignment #3 is due Feb 24, 10:30am

York University
Professor Mike Zabrocki
MWF 10:30-11:30am FC-034C
Office: Ross S615
Office hours: W4-5pmF11:30am-12:30pm
or by appointment
Best way to contact me:

Topics: algebra of sets, permutations, combinations, occupancy problems, partitions of integers, generating functions, combinatorial identities, recurrence relations, inclusion-exclusion principle, Polya's theory of counting, permanents, systems of distinct representatives, Latin rectangles, block designs, finite projective planes, Steiner triple systems.

Prerequisites: AS/SC/AK/MATH 2022 3.0 or AS/SC/AK/MATH 2222 3.0; six credits from 3000-level MATH courses (without second digit 5); or permission of the course coordinator.

Text: An introduction to combinatorics by Alan Slomson

The grade in this course will be based on the following criterion:
1. Homework (5) 20%
2. Midterm exams (2) 40%
3. Final exam 40%

The homework is for your benefit so it is in your interest to spend some time doing the problems each week.  Struggle with them for a while before getting help from either myself, the TA, or your fellow students.  Do not copy homework assignments.

Topic/sections in text
Basic counting principles

More basic counting
HW #1
Combinatorial proofs inclusion-exclusion
HW #2

Partitions and generating functions
Alt exam
MT #1 problem #4 HW2
Partitions and generating functions
HW #3

Reading week

Alt exam
Generating functions
HW #4
HW #3
Generating functions, take home 2nd midterm

HW #4
HW #5
MT #2
the group of permutations

permutations and symmetry

Polya enumeration

HW #5

In class handouts (if you missed a day or lost your copy, they should all be here):
  1. syllabus (1/6/03)
  2. in class problem set #1 (1/8/03)
  3. A list of poker hands and descriptions
  4. Homework set #1 - due 1/24/03 (1/13/03)
  5. Odds for the Lottery - 6/49 Super 7 Encore (1/20/03)
  6. Inclusion-exclusion problems (1/24/03)
  7. Homework #1 solutions (1/24/03)
  8. Practice for the midterm (1/27/03)
  9. Second homework assignment
  10. Midterm #1 (1/31/03)
  11. Alternate midterm #1 (2/5/03)
  12. Solution to problem #4 on midterm #1 (2/6/03)
  13. Homework #2 solutions (2/6/03)
  14. Homework #3 (2/6/03)
  15. Solution to the alternate exam (2/19/03)
  16. Homework #4 (2/20/03)
  17. Homework #3 solutions (2/24/03)
  18. Practice for 2nd midterm (2/28/03)
  19. F. Franklin's proof of Euler's pentagonal number theorem (2/28/03)
  20. Solutions to Homework #4 (3/7/03)
  21. Midterm #2 - take home (3/7/03)
  22. Midterm #2 - solutions (3/12/03)
  23. Homework 5 (3/14/03)
  24. Practice for final (3/14/03)
  25. The Rotational symmetries of the cube (3/2/03)
  26. Solutions to Homework #5 (3/4/03)
  27. Take home final exam (3/4/03)
  28. Cover sheet for final exam (3/4/03)
  29. Grad student final exam (3/4/03)

Interesting and related:
  1. Richard Stanley's list of combinatorial interpretations of the Catalan numbers (see the excerpt of the EC2)
  2. The On-Line Encyclopedia of Integer Sequences