The course is over, and you can pick up your corrected assignments from the student expedition unless I told you something else by email.

SF2708 Kombinatorik, 7.5 credits

Content: We will study basic techniques in enumerative combinatorics. Examples include the twelvefold way (i.e. counting functions subject to various restrictions), sieve methods such as various versions of the inclusion-exclusion principle, the involution principle and determinantal lattice path counting. We also take a peek into the rich theory of partially ordered sets (posets). Our initial motivation is the general Möbius inversion theorem for posets which is a common generalisation of the Möbius inversion theorem from number theory and the principle of inclusion-exclusion, but posets turn out to have many more applications.

Essentially, we will cover the first three chapters in Stanley's book with the exception of Sections 2.5 and 3.15-16.

Consult the study handbook for more information.

Literature:
[St] Richard P. Stanley, Enumerative Combinatorics, Volume I, 2nd edition, Cambridge University Press, 1998.
[Wa] An excerpt from Michelle L. Wachs, Poset topology: Tools and applications, math.CO/0602226.
Here is a complement to [Wa] for people with no background in topology.

Examination and grading: Four sets of homework problems will be handed out.

Problem set 1. Deadline: March 14.
Problem set 2: PDF, TeX. Update in Problem 9 (March 25). Deadline: April 11.
Problem set 3: PDF, TeX. Update in Problem 9 (April 14). Deadline: April 28.
Problem set 4: PDF, TeX. Deadline: May 23.

Here is how the grading works:

Undergraduate students: Solving roughly 85% of the problems gives grade B, 75% &ndash C, 65% &ndash D, 55% &ndash E, 50% &ndash 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.

Schedule: Most lectures take place on Fridays 13.15–15.00 in room 3733, Department of Mathematics, KTH, Lindstedtsvägen 25, floor 7. In addition, there will be a few lectures on Mondays in room 3721, same time and address. The following schedule is preliminary and will be continuously adjusted:

Update: On Mondays marked with "*", the time is 14.15–16.00.

Date Room We did/plan to do:
Jan 25 3733 Introduction, St1.1
Feb 1 3733 St1.2, parts of St1.3
Feb 8 3733 St1.3, most of St1.4
Feb 22 3733 St1.4, St2.1, parts of St2.2
Feb 29 3733 St2.2, most of St2.3
Mar 14 3733 St2.3–4, some of St2.6, problem set 1 was due
Mar 28 3733 St2.6, most of St2.7
Apr 4 3733 St2.7, St3.1
Apr 7* 3721 St3.2, parts of St3.3
Apr 11 3733 LECTURE CANCELLED
Apr 14 3721 St3.3–4, problem set 2 was due
Apr 18 3733 St3.5–6, parts of St3.7
Apr 21* 3721 St3.7, parts of St3.8 and Wa
Apr 25 3733 Wa, St3.8, parts of St3.9–10 via Crapo's theorem (St, Exc 3.30)
Apr 28 3721 St3.9–10, problem set 3 was due
May 5* 3721 St3.11, most of St3.12
May 9 3733 St3.12, most of St3.13
May 16 3733 St3.13–14
May 23   No lecture, problem set 4 and summary were due
Axel Hultman