## Math 824 (Algebraic Combinatorics) Fall 2018

### General Information

• Instructor: Jeremy Martin
• E-mail: (the best way to contact me)
• Office: 618 Snow Hall, (785) 864-7114
• Office hours: Thursdays, 1-3pm
• Lectures: MWF, 1:00-1:50pm, 456 Snow
• Prerequisite: Math 724 (Enumerative Combinatorics) or permission of the instructor. Math 790 (Linear Algebra) is not an official requirement but is strongly encouraged.
• KU course number: 27817
• Syllabus

### 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.

• Problem Set #1, due August 31: 1.1, 1.3, 1.4, 2.1, 2.4, 2.5, 2.7
• Problem Set #2, due September 14: 2.9, 2.10, 2.11, 3.1, 3.8
• Problem Set #3, due September 28: 3.4, 3.7, 4.1, 4.2, 4.4, 4.6
• Problem Set #4, due October 19 October 22: 4.7 or 4.10 (your choice); 5.1, 5.4, 6.2, 6.3
• Problem Set #5, due November 19: 7.3, 7.4, 9.1, 9.2, 9.5, 9.6, 9.7
• Problem Set #6, due December 5: 10.1, 10.2, 10.4, 10.5

### Textbooks

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)
2. Richard P. Stanley, Enumerative Combinatorics, volume 2 (Cambridge, 1999)
(More enumeration, including exponential generating functions; symmetric functions)
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

• The assignment. Everyone should meet with Jeremy and finalize their topic choice no later than Monday, October 29.
• The schedule of talks and reviewers is below. If the links to papers don't work, try searching for the paper using MathSciNet (requires KUID).