MATH 249 – Algebraic combinatorics, Fall 2019
Class times: M, W, F 10:1011:00, 740 Evans.
Office hours: M, F 11:0012:00, 933 Evans.
Instructor: Sylvie Corteel
email: lastname at berkeley dot edu
Course homepage: math.berkeley.edu/~corteel/MATH249.html
Office: 859 Evans
Other combinatorial activities (please register) MATH 290 Research seminar CCN15370 MATH 290 Reading seminar CCN15355Textbook: The art of counting^{ } by Bruce Sagan
Further reading: Enumerative Combinatorics 1 and 2, by Stanley. Algebraic combinatorics by Stanley. The symmetric group by Bruce Sagan. Young tableaux by Fulton. A course in enumeration by Aigner.
Prerequisites: Math 55, 110, 113, 172
Grading: Homework
– 50%, Presentation – 25% each, Final paper – 25%
Homework Policies: Homework will typically be assigned every other week and collected the following at the beginning of the class. No homework will be accepted after class for any reason. You may work together on homework problems, but your solutions should be written up independently and answers must be given in understandable form.
Special accommodations: In case of disability, extracurricular activities, or religious holidays, please follow official university procedure.
Date 
Topics 
Reading 
Homework 
08/28 and 08/30 
Fibonacci numbers, permutations and trees 
Chapter 1 

09/04 and 09/06 
Trees, partitions, lattice paths 
Chapter 1 
Homework 1 due 9/18 
09/09, 09/11, 09/13, 09/16 
Counting with signs: inclusionexclusion, sign reversing involutions, Reflection principle, LGV lemma, Matrix tree theorem 
Chapter 2 

09/18, 09/20, 09/23, 09/25 
Ordinary generating functions 
Chapter 3 
Homework 2 due October 14 
09/27, 09/30, 10/02 
Exponential generating functions. Lagrange inversion 
Chapter 4 (Sagan) Chapter 5 (Enumerative Combinatorics 2 by Stanley) 

10/04, 10/07, 10/09 (cancelled  power outage), 10/11 (cancelled  power outage) 
Symmetric functions 
Chapter 7 
Homework 3 due October 28 
10/14, 10/16, 10/18, 10/21, 10/23, 10/25 
Symmetric functions (cont.), Vertex operators 
Chapter 7 (Sections 7.2, 7.3 and 7.8) Chapter 5 of Guillaume Chapuy's notes 

10/28 (cancelled power outage), 10/30, 11/01, 11/04 
Symmetric functions (cont.): Ppartitions, RSK algorithm 
Chapter 7 (Sections 7.4 and 7.6) 
Homework 4 due 11/13 
11/06, 11/08, 11/11 (no class, holiday) 
Generalizations of Schur polynomials: skew Schur, Hall Littlewood 
Stanley Chapter 5 Section 7.9, 7.10, Appendix 1.3 Stanley Chapter 5 Chapter 3 

11/13, 11/15, 11/18, 11/20 
Chromatic symmetric functions, Group actions, Cyclic Sieving phenomenon 
Sagan: section 7.9, sections 6.1, 6.2, 6.6, appendix A, 7.10. Survey paper on cyclic sieving phenomenon 

11/22 and 11/25 
Quasisymmetric functions. Mobius inversion 
Sagan: sections 8.1 and 8.2. sections 5.1, 5.4 and 5.5 Survey paper (extra reading) 
Homework 5 due 12/04 
12/02, 12/04 
Quasisymmetric functions 
Sagan: sections 8.3, 8.5 and 8.6.


12/06 and 12/09 
Presentations (15min per person) 
Paper is due on 12/13 