This is the page of the combinatorics course MTH318, which I am teaching in IISER Pune in the fall semester Aug-Nov 2018. We will have two lectures (on Tuesday's and Thursday's), and one tutorial (on Friday's). All the assignments, lecture notes, and related stuff will be posted here. The following books will be the references for this course:
Introductory Combinatorics (Fifth Edition, 2010), Richard A. Brualdi.
Combinatorics (1994), Peter J Cameron.
Enumerative Combinatorics (Vol 1 and 2), Richard Stanley.
Some notes by Peter Cameron.
I will primarily be teaching from Brualdi, but will use Stanley's and Cameron's books for certain topics.
My Zimbra account is up and running, so if you want to write to me regarding anything, you can continue to email me on zimbra, or else on my gmail id: udaybsharmaster@gmail.com.
Lecture 1 (02-08-2018): Why combinatorics, what is combinatorics, some examples of arrangements.
Lecture 2 (03-08-2018): Multisets: Lecture Notes and Exercises.
3. Lecture 3 (07-08-2018): Multisets Lecture Notes and Exercises.
4. Lecture 4 (09-08-2018): Pigeonhole Principle: Lecture Notes and Exercises.
5. Lecture 5 (14-08-2018): Pigeonhole Principle: Lecture Notes.
6. Lecture 6 (16-08-2018): Partially Ordered Sets. Lecture Notes.
PS: In the lecture I made an error in a definition, that of weak-subposet. It should've been s < t in Q implies s < t in P (and not the other way round, which I mentioned in class). Apologies for that error. The correct definition is in the notes.
Here is the Exercise Set for this week.
7. Lecture 7 (21-08-2018): Partially Ordered Sets. Lecture Notes
8.Lecture 8 (23-08-2018): Lattices. Lecture Notes.
9. Lecture 9: Lattices, Mobius Functions. Lecture Notes.
10. Lecture 10: Mobius Functions. Lecture Notes.
11. Lecture 11: Mobius Functions. Lecture Notes.
12Lecture 12: Principle of Inclusion and Exclusion. Lecture Notes.
Exercises on Lattices and Mobius Functions.
13. Lecture 13: Principle of Inclusion and Exclusion. Lecture Notes.
14. Lecture 14: Recurrence Relations. Lecture Notes.
15. Lecture 15: Recurrence Relations. Lecture Notes.
Here are some Exercises related to Recurrence Relations.
16. Lecture 16: Generating Functions. Lecture Notes.
17. Lecture 17: Generating Functions. Lecture Notes.
18. Lecture 18: Generating Functions. Lecture Notes.
A set Exercises related to all that we have covered in generating functions.
19. Lecture 19: Burnside's Lemma and Polya's Theorem. Lecture Notes.
20. Lecture 20: Burnside's Lemma and Polya's Theorem. Lecture Notes.
Here are some Exercises on Generating Functions, and Burnside-Polya.
21. Burnside's Lemma and Polya's Theorem. Lecture Notes.
22. Burnside's Lemma and Polya's Theorem. Lecture Notes.
23. Burnside's Lemma and Polya's Theorem. Lecture Notes.
24: Symmetric Functions: An Introduction. Lecture Notes.
A final Exercise Set for this semester, on Polya-Burnside stuff.