Math 824 (Algebraic Combinatorics)
Fall 2012

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

General Information

Lecture Notes

Lecture notes (one big PDF file; last update 12/3/12)

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 day by day, with approximate page numbers

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.

Problem Set #1 (due Wed 9/3/12): PDF | LaTeX
Problem Set #2 (due Fri 9/21/12): PDF | LaTeX
Problem Set #3 (due Fri 10/5/12): PDF | LaTeX
Problem Set #4 (due Fri 10/26/12): PDF | LaTeX
Problem Set #5 (due Mon 12/3/12): PDF | LaTeX


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)
    You can buy it from the publisher or use the free preprint version on Stanley's website.
  2. R.P. Stanley, Enumerative Combinatorics, volume 2 (Cambridge, 1999)
    (More enumeration, including exponential generating functions; symmetric functions)
    Amazon | Google Books
  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, 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 talk. Here are full details and some suggestions for articles to read.

The presentations will take place on Thursday 12/13 and Friday 12/14. Here is the schedule (subject to change):

Thursday 12/13, 1:30-4:00 PM, Snow 456
Time Presenter Paper Reviewer
1:30-1:50 Billy Sanders J. Eagon and V. Reiner, Resolutions of Stanley-Reisner rings and Alexander duality Nick
2:00-2:20 Tony Se A. Van Tuyl and R. Villarreal, Shellable graphs and sequentially Cohen-Macaulay bipartite graphs Alex
2:30-2:50 Alex Lazar W. Schmitt, Incidence Hopf algebras Ilya
3:00-3:20 Nick Packauskas M. d'Adderio and L. Moci, Arithmetic matroids, the Tutte polynomial and toric arrangements Billy
3:30-3:50 Khoa Le Y. Chan, J.-F. Marckert and T. Selig, A natural stochastic extension of the sandpile model on a graph Tony
Friday 12/14, 10:30-1:00 PM, Snow 564
Time Presenter Paper Reviewer
10:30-10:50 Logan Godkin F. Ardila, Computing the Tutte polynomial of a hyperplane arrangement Khoa
11:00-11:20 Ilya Smirnov C. Klivans and E. Swartz, Projection volumes of hyperplane arrangements Rob
11:30-11:50 Rob Bradford C. Athanasiadis, A combinatorial reciprocity theorem for hyperplane arrangements Logan
12:00-12:20 C.J. Harries S. Chestnut and D. Fishkind, Counting spanning trees of threshold graphs John
12:30-12:50 John Reynolds S. Hopkins and M. Weiler, Pattern avoidance in permutations on the Boolean lattice C.J.


KU links

Software and online resources

Last updated Wed 12/5/12 3:30 PM