# Algebraic and enumerative combinatorics (graduate course)

This course is on techniques in algebraic and enumerative combinatorics. Focus is on generating functions and the combinatorics of symmetric functions, partly following R. P. Stanley, Enumerative combinatorics Vol 2, chapters 5-7.

**Lecturer:** Petter Brändén. Email: pbranden "at" kth "dot" se

**Prerequisites:** Basic courses in algebra and combinatorics, mathematical maturity.

**When and where:** Tuesdays at 10:15 in room 3721 at KTH.

### Some literature

The main reference is chapters 5-7 in R. P. Stanley, Enumerative combinatorics Volume 2.

Richard P. Stanley, Enumerative Combinatorics, Vol 2, Cambridge University Press

I. G. Macdonald, Symmetric functions and Hall polynomials, Oxford Mathematical Monographs

### Examination

Two sets of homework problems will be handed out.

Homework 1. To be handed in March 1. HW1

Homework 2. To be handed in May 24. HW2

### Plan/What we have done

19/1: Introduction. Formal power series. Rational and algebraic series. Ch. 6.1-6.2 Notes

26/1: Rational, algebraic and D-finite series. Noncommutative formal series Ch. 6.3-6.5 Notes

2/2: Rational noncommutative series Ch. 6.5 Notes

9/2: Algebraic noncommutative series Ch. 6.6 Notes

16/2: Algebraic noncommutative series, continued Ch. 6.6 Notes

23/2: Symmetric functions. Ch. 7.1-7.5. Notes

1/3: Symmetric functions. Ch. 7.6-7.10. Notes

8/3: Symmetric functions. Ch. 7.10-7.11. Notes

15/3: Symmetric functions. Ch. 7.11-7.13. Notes

22/3: Symmetric functions. Ch. 7.14-7.15. Notes

29/3: Symmetric functions. Ch. 7.16-7.17. Notes

12/4: Symmetric functions. Ch. 7.19. Notes

19/4: Symmetric functions. Ch. 7.19-7.21. Notes

26/4: Symmetric functions. Ch. 7.21-7.23. Notes

10/5: Symmetric functions. Ch. 7.23, Paper, Paper, Notes