Most of the problems are assigned from the required textbook Bona, Miklos. A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory. World Scientific Publishing Company, 2011. ISBN: 9789814335232. [Preview with Google Books]
A problem marked by * is difficult; it is not necessary to solve such a problem to do well in the course.
Problem Set 3

Due in Session 8

Practice Problems
 Session 6: Chapter 5: Exercises 11, 12, 13
 Session 7: Chapter 5: Exercises 1, 5, 16

Problems Assigned in the Textbook
 Chapter 5: Exercise 21
 Chapter 5: Exercise 34. Only do the case k=1, which is already pretty tricky and in my opinion deserves a (+)

Additional Problems
 (A2) Let λ be a partition with conjugate λ’. Show that
Σ _{i} ⌊λ2__{i1}_/2⌋ = Σ _{i} ⌈λ’_{2i}/2⌉.
This can be seen almost by inspection from the Young diagram of λ after certain marks are made on it. Note. The notation ⌊x⌋ means the greatest integer ≤_x_. For instance, ⌊3⌋=3, ⌊3/2⌋=1. Similarly ⌈x⌉ means the least integer ≥_x_. For instance, ⌈3⌉=3, ⌈3/2⌉=2. (A3) Show by simple combinatorial reasoning and induction that the Bell number B(n) is even if and only if n2 is divisible by 3.

Bonus Problems
 None