Math 824 (Algebraic Combinatorics)
Fall 2018

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

General Information

Lecture Notes

Lecture Notes on Algebraic Combinatorics (1.7MB PDF file; last update 11/28/18)

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!

Schedule of topics (subject to change):

Problem Sets

Problem sets will be assigned approximately biweekly, at least one week before the deadline.

All solutions must be typeset using LaTeX. E-mail me your solutions as a PDF file under the name {your-last-name}{number-of-problem-set}.pdf (e.g., "Rota5.pdf"). Unless otherwise specified, the deadline is 11:59pm on the due date. Late homework will not be accepted.

Make sure you have the most recent version of the lecture notes before starting each problem set, just in case the numbering has changed.

Additional resources:


We will follow the lecture notes rather than any one specific textbook. 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. Richard P. Stanley, Enumerative Combinatorics, volume 1, 2nd ed. (Cambridge, 1997)
    (Enumeration; posets and lattices; generating functions)
    Buy it from the publisher or download the free preprint version from Stanley's website
  2. Richard P. Stanley, Enumerative Combinatorics, volume 2 (Cambridge, 1999)
    (More enumeration, including exponential generating functions; symmetric functions)
    Buy it from the publisher
  3. Martin Aigner, A Course in Enumeration (Springer, 2007)
    (Enumeration; posets, lattices, and matroids)
  4. Martin Aigner, Combinatorial Theory (Springer, 1997)
    (Enumerative combinatorics, symmetric functions, and matroids)
  5. Richard P. Stanley, Hyperplane Arrangements (lecture notes available free online)
  6. Alexander Schrijver, A Course in Combinatorial Optimization (lecture notes available free online)
  7. Thomas Brylawski and James Oxley, The Tutte polynomial and its applications, Chapter 6 of Matroid applications, N. White, ed. (Cambridge Univ. Press, 1992)
  8. Matthias Beck and Raman Sanyal, Combinatorial Reciprocity Theorems: A Snapshot of Enumerative Combinatorics from a Geometric Viewpoint (manuscript available free online)
  9. Bruce E. Sagan, The Symmetric Group, 2nd edn. (Springer, Graduate Texts in Mathematics, 203, 2001)
  10. Federico Ardila, Algebraic and geometric methods in enumerative combinatorics (free book; covers much of the same material as my notes but from a slightly different perspective, and probably a more polished presentation)

Final Project


KU links

Software and online resources

Last updated Wed 11/28/18