Math 824 (Algebraic Combinatorics)
Fall 2016

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

General Information

Lecture Notes

Lecture Notes on Algebraic Combinatorics (one big PDF file; last update 12/7/16)

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!

Lecture topics, day by day:

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"). In general, the deadline is 11:59pm of the due date.

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 Sagan, The Symmetric Group, 2nd edn. (Springer, 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

Date Presenter Reviewer Paper
December 5 Smita Praharaj Amanda Wilkens A. Knutson and T. Tao
Honeycombs and sums of Hermitian matrices
Notices Amer. Math. Soc. 48, no. 2 (2001), 175-186.
December 5 Amanda Wilkens Smita Praharaj B.E. Sagan
Probabilistic proofs of hook length formulas involving trees
Sém. Lothar. Combin. 61A (2009/10), Art. B61Ab, 10 pp.
December 14 Brandon Caudell Connor Smith J. Edmonds
Minimum partition of a matroid into independent subsets
J. Res. Nat. Bur. Standards Sect. B 69B (1965), 67-72.
December 14 Joseph Doolittle Brandon Caudell R.P. Stanley
Two poset polytopes
Discrete Comput. Geom. 1 (1986), 9-23.
December 14 Arturo Jaramillo Bibekananda Mishra A. Nica and R. Speicher
Non-crossing partitions and free cumulants
From Lectures on the combinatorics of free probability (Cambridge U. Press, 2006), pp. 135-194 (mainly pp. 173-194)
December 14 Bibekananda Mishra Joseph Doolittle P. Orlik and L. Solomon
Combinatorics and topology of complements of hyperplanes
Invent. Math. 56 (1980), no. 2, 167-189.
December 14 Connor Smith Arturo Jaramillo A. Goodall
Fourier analysis on finite Abelian groups: some graphical applications
From Combinatorics, Complexity and Chance: a tribute to Dominic Welsh (G. Grimmett and C. McDiarmid, eds.), Oxford U. Press, 2007, 103-129.


KU links

Software and online resources

Last updated Fri 12/9/16 8:00am