Math 824 (Algebraic Combinatorics)
Spring 2015

General Information | Lecture Notes | Problem Sets | Textbooks | Final Project | Links

General Information

Lecture Notes

Lecture notes (one big PDF file; last update 4/29/15) [Newer version available from my homepage]

These notes are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. In short, use them freely but do not sell them or anything derived from them. If you are a KU graduate student (or for that matter, if you aren't), do not print out the full set of notes on the department's printer!

Material covered each day:

Problem Sets

All solutions must be typeset using LaTeX.

E-mail me the PDF file under the name {your-last-name}{number-of-problem-set}.pdf (e.g., "Rota5.pdf").


We will follow the lecture notes rather than any one specific textbook and all of the homework assignments will be self-contained. However, the following books may be helpful (and you should definitely obtain the free downloads). All these books can be perused in Jeremy's office.

  1. R.P. Stanley, Enumerative Combinatorics, volume 1, 2nd ed. (Cambridge, 1997)
    (Enumeration; posets and lattices; generating functions)
    Buy it from the publisher
    Download the free preprint version from Stanley's website
  2. R.P. Stanley, Enumerative Combinatorics, volume 2 (Cambridge, 1999)
    (More enumeration, including exponential generating functions; symmetric functions)
    Buy it from the publisher
  3. M. Aigner, A Course in Enumeration (Springer, 2007)
    (Enumeration; posets, lattices, and matroids)
  4. M. Aigner, Combinatorial Theory (Springer, 1997)
    (Enumerative combinatorics, symmetric functions, and matroids)
  5. R.P. Stanley, Hyperplane Arrangements (lecture notes available free online)
  6. A. Schrijver, A Course in Combinatorial Optimization (lecture notes available free online)
  7. T. Brylawski and J. Oxley, The Tutte polynomial and its applications, Chapter 6 of Matroid applications, N. White, ed. (Cambridge Univ. Press, 1992)
  8. M. Beck and R. Sanyal, Combinatorial Reciprocity Theorems: A Snapshot of Enumerative Combinatorics from a Geometric Viewpoint (manuscript available free online)
  9. B. Sagan, The Symmetric Group, 2nd edn. (Springer, 2001)

Final Project

The final project is to read a current research article in combinatorics, write a short, self-contained summary (1 page), give a short talk on it (20 minutes, like an AMS special session talk) to an audience of fellow graduate students, and provide constructive criticism on another student's project. Complete details are here. Everyone should meet with Jeremy individually to select a paper to read, no later than April 10.

Time Speaker Paper Reviewer
10:30 Ken Duna A. Brouwer, S. Cioaba, W. Haemers and J. Vermette
Notes on simplicial rook graphs
Lucas Chaffee
10:55 Brent Holmes F. Santos, T. Stephen and H. Thomas
Embedding a pair of graphs in a surface, and the width of 4-dimensional prismatoids
Discrete Comput. Geom. 47 (2012), no. 3, 569-576.
Josh Fenton
11:20 Josh Fenton F. Ardila
Computing the Tutte polynomial of a hyperplane arrangement
Pacific J. Math. 230, no. 2 (2007), 1-26.
Kevin Adams
11:45 Lucas Chaffee C. Greene, H. Nijenhuis and H. Wilf
A probabilistic proof of a formula for the number of Young tableaux of a given shape
Adv. Math. 31 (1979), 104-109.
Brent Holmes
1:00 Bennet Goeckner C. Klivans
Obstructions to shiftedness
Discrete Comput. Geom. 33 (2005), 535-545.
Ken Duna
1:25 Kevin Adams B. Braun and R. Ehrenborg
The complex of non-crossing diagonals of a polygon
J. Combin. Theory Ser. A 117 (2010), 642-649.
Bennet Goeckner


KU links

Software and online resources

Last updated Sat 5/16/15