| Subject |
Combinatorial Mathematics |
| Title |
Enumerative and Asymptotic Combinatorics |
| Lecturer |
Prof P.J. Cameron |
| Code |
MTHM C50 |
| Level |
(b) |
| Hours |
2 |
| Semester |
2 |
| Week |
13 January 2003 |
| Syllabus |
-
Techniques: Inclusion-exclusion,
recurrence relations and generating functions.
-
Subsets, partitions, permutations: binomial coefficients; partition,
Bell, and Stirling numbers; derangements. q-analogues: Gaussian
coefficients, q-binomial theorem.
-
Linear recurrence relations with constant coefficients.
-
Counting up to group action: Orbit-counting 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.
|
| Texts |
-
R. P. Stanley, "Enumerative Combinatorics", Vol. 1, Cambridge University
Press, 2000.
-
A. M. Odlyzko, Asymptotic enumeration methods, pp. 1063-1230 in
"Handbook of Combinatorics" (ed. R. L. Graham, M. Grötschel
and L. Lovász), North Holland, 1995.
|
| Timetable |
Wednesdays 10:00-12:00, Mathematics 103 (MSR)
Class Thursdays 14:00-15:00, Mathematics 513 |
|
Web page
|
http://www.maths.qmul.ac.uk/~pjc/C50/
|