Math
4160  Combinatorial Mathematics

Professor: Mike Zabrocki email: Meetings: TuesThurs 2:304pm HNE B15 Office hours: TEL 2028  Monday 12:302:30pm, Thursday 45pm Textbook: Bijective Combinatorics  Nicolas A. Loehr 
What is the rule?

assignments  55% 
midterm  20% 
final  25% 
Lecture 
dates 
Topic/sections in text 
notes/relevant handouts 
1 
Thurs, Sept 6 
sums, Stirling numbers, addition/multiplication principle 

2 
Tues, Sept 11 
from $\sum_{i=1}^n i = n(n+1)/2$ to $\sum_{i=1}^n i^r = \sum_{k=1}^r S(r,k) (n)_k$ 

3 
Thurs, Sept 13 
basic counting  $n!$, ${n \choose k}$, $S(n,k)$, $s'(n,k)$, $B(n)$ 

4 
Tues, Sept 18 
basic counting, cards and combinatorial identities 

5 
Thurs, Sept 20 
distributions and multichoose 

6 
Tues, Sept 25 
proving combinatorial identities, beginning of generating functions 

7 
Thurs, Sept 27 
generating functions 
Hw #1 due,
some problems for next time,
Hw #2 assigned 
8 
Tues, Oct 2 
more generating functions 

9 
Thurs, Oct 4 
generating functions and combinatorics 
hw #1 returned 
10 
Tues, Oct 9 
review for midterm 
note office hours 45pm today 
11 
Thurs, Oct 11 
Midterm  take home 
office hours cancelled today, available Monday 10:30am  4:30pm 
12 
Tues, Oct 16 
generating functions, exponential generating functions, partitions 
Hw #2 due, midterm due 
13 
Thurs, Oct 18 
partitions, exponential generating functions and combinatorics 
matching partition gfs, Hw #3 assigned Oct 20 (revised Oct 28) 
14 
Tues, Oct 23 
partition generating functions 
matching partition gfs, partition gfs 
15 
Thurs, Oct 25 
partition generating functions, introduction to groups 
partition gfs, midterm returned 
16 
Tues, Oct 30 
coloring a cube, motions of a triangle/square as a group 
homework #2 returned 
Thurs, Nov 1 
no class 

17 
Tues, Nov 6 
the group of motions of the cube, group actions 
Hw #3 due 
18 
Thurs, Nov 8 
group actions, equivalence relations, the orbitstabilizer theorem 

19 
Tues, Nov 13 
Justified the orbitstabilizer theorem 
Hw #4 assigned 
20 
Thurs, Nov 15 
Burnside's Lemma, Polya's theorem 
Returned HW #3 
21 
Tues, Nov 20 
necklaces, permutations of a given cycle type 

22 
Thurs, Nov 22 
coloring spoke graph, permutations of a given cycle type 

23 
Tues, Nov 27 
remarks about hw#4, permutations 

24 
Thurs, Nov 29 
an application of Burnside's lemma, Catalan numbers and Dyck paths 
Hw #4 due 