MTHM030/MTH710U 
Enumerative and Asymptotic Combinatorics 
Course Material 
January  April 2011 
The syllabus for the course is:
 Techniques: inclusionexclusion, recurrence relations and generating
functions.
 Subsets, partitions, permutations: binomial coefficients; partition, Bell,
and Stirling numbers; derangements. qanalogues: Gaussian coefficients,
qbinomial theorem.
 Linear recurrence relations with constant coefficients.
 Counting up to group action: orbitcounting lemma, cycle index theorem.
 Posets and Möbius inversion, Möbius function of projective space.
 Asymptotic techniques: order notation: O, o, ~. Stirling's
formula. Techniques from complex analysis including Hayman's Theorem.
The course will be based roughly on the contents of Peter Cameron's notes
from the
2006 course, which are available here.
However, there is a new version of the notes
(last updated 18 February 2010), which he intends to publish.
The current plan is to cover the following sections in the
new version of the notes:
 1.1, 1.2
 2.2, 2.5
 3.1, 3.2, 3.3
 4.1, 4.3
 4.2, 4.4, 4.5
 6.1, 6.2, 6.3
 7.1, 7.2, 7.3
 8.1, 8.2, 8.3, 8.4
 10.1
 11.4
Exercises
There are many exercises given at the end of each chapter in
Peter's notes. You should think about all the exercises which are
relevant to the above sections of the notes. You should hand in
solutions to the following exercises from the new version of the notes at
our weekly meetings.
 Week 2: Exercises 1.2, 1.3 Solutions
 Week 3: Exercises 2.1, 2.13, 2.14 Solutions
 Week 4: Exercises 3.1, 3.2, 3.6, 3.10
 Week 5: Exercises 3.11, 3.20, 3.23, 3.24
Solutions
 Week 6: Exercises 4.3, 4.4, 4.5, 4.9
 Week 7: Exercises 4.10, 4.11, 4.12
Solutions
 Week 8: Exercises 6.3, 6.4, 6.5
Solutions
 Week 9: Exercises 7.1, 7.3, 7.5, and fill in the missing step in the
proof of Theorem 7.2.
Solutions
 Week 10: Exercises 8.1, 8.3, 8.4, 8.7
 Week 11: Exercises 10.1, 11.2
Other web resources:

The book Analytic Combinatorics by Flajolet and Sedgwick is
free to download
here
(but it is over 800 pages long!)

Another freetodownload book on enumerative combinatorics is
A=B, by Petkovsek,
Wilf and Zeilberger; this discusses a computational method for proving
complicated identities.
Past exam papers
A sample exam paper and six past exam papers
are here: 2003 exam, 2005 exam,
2006 exam, 2008 exam,
2009 exam, and 2010 exam.
Note that there was a typo in Q1(d) 2010: P and Q should be exponential
generating functions and the required identitiy should be P(x)=Q(exp(x)1)