Where and when: Tuesdays at 13:15-15:00 in room 3733.
Instructor: Petter Brändén, room 3626
Credits: 7.5, Grades: A-F, Language: English
Literature: R. P. Stanley, Enumerative Combinatorics, second edition, Cambridge University Press, 2011 (Electronic copy available at Stanley's homepage).
Contents: Basic methods in enumerative combinatorics. Sieve methods, for example inclusion-exclusion, the involution principle and the method of using determinants to count lattice paths. Various aspects of the theory of partially ordered sets, for example lattice theory, Möbius inversion in posets, P-partitions, and connections to topology.
Examination and grading: Four sets of homework problems will be handed out. Here is how the grading works:
Undergraduate students: Solving roughly 85% of the problems gives grade B, 75% gives C, 65% gives D, 55% & gives E, 50% gives Fx. In addition, one can choose to do a voluntary assignment which consists of writing a summary of a research article. Details about this assignment and articles to choose from can be found here. If satisfactory written, the summary will raise one's grade by one step.
Graduate students: In order to pass, one must solve 70% of the homework problems and hand in a satisfactory summary of a research article.
Homework: Collaboration is allowed, but you should write the solutions yourself. Please show all your work!
HW1. (To be handed in Feb. 28): Exercises from Stanley 1: 1.12 (Hint: Use Euler's formula for planar graphs), 1.20, 1.26, 1.33a, 44a, 47ab, 102abc, 114ab, 121ab.
HW2. (To be handed in March 20): PDF
HW3. (To be handed in April 17): PDF
HW4. (To be handed in May 22): PDF
Schedule:
| Date | Plan |
|---|---|
| 01-19 | Ch. 1.1-1.2. |
| 01-24 | Ch. 1.1-1.3. |
| 01-31 | Ch. 1.3-1.4. |
| 02-07 | Ch. 1.7-1.9, 2.1-2.2. |
| 02-14 | Ch. 2.1-2.2, 2.7 |
| 02-21 | NO CLASS! |
| 02-27 | Ch. 2.7, 3.1-3.2 |
| 03-06 | Ch. 3.2-3.4 |
| 03-13 | Ch. 3.4-3.8 |
| 03-20 | Ch. 3.8-3.11 |
| 03-27 | Ch. 3.11 |
| 04-03 | NO CLASS! |
| 04-10 | Ch. 3.11, Ch. 3.15. Notes from class: PDF. Exposition differs slightly from book. |
| 04-17 | Ch. 3.15, 3.12, 3.13 |
| 05-01 | NO CLASS! Public Holidays |