Section 78865

Basic Information | Problem Sets | Lecture Notes | Final Exam / Project | Textbooks | Links

**Instructor:**Jeremy Martin

541 Snow, 864-7114- Syllabus (PDF)
**Meeting times:**MWF, 12:00-12:50 PM, 408 Snow**Office hours:**Tue 11:00-12:00 and Wed 2:00-3:00, or by appointment**Prerequisite:**Math 724 (Enumerative Combinatorics) or permission of the instructor

Problem Set #1 (due Friday 2/1/08)

Problem Set #2 (due Friday 2/15/08)

Problem Set #3 (due Friday 2/29/08)

Problem Set #4 (due Friday 3/14/08)

Problem Set #5 (due Friday 4/11/08)

Problem Set #6 (due Wednesday 5/6/08)

Posets: definition and examples (1/18)

More posets; lattices (1/23)

Lattices and distributive lattices (1/25)

Birkhoff's theorem on distributive lattices (1/28)

Modular lattices (1/30)

Semimodular lattices (2/1)

Geometric lattices (2/4)

Matroids and geometric lattices; uniform and graphic matroids (2/8)

Graphic matroids; basis and independence systems (2/11)

Circuit systems; duality (2/13)

Direct sum; deletion and contraction (2/15)

The Tutte polynomial I (2/18)

The Tutte polynomial II (2/20)

The Tutte polynomial III (2/22)

The incidence algebra and the Möbius function (2/25)

Möbius inversion; the characteristic polynomial (2/27)

The Möbius algebra of a lattice, and applications (2/29)

The crosscut theorem; introduction to hyperplane arrangements (3/3)

Counting regions I: examples and deletion/restriction (3/5)

Counting regions II: Zaslavsky's theorems and finite fields (3/7)

Projectivization and coning; complex arrangements; graphic arrangements (3/10)

Modular elements in lattices; supersolvable arrangements (3/12)

The big face lattice of an arrangement (3/24)

Oriented matroids (3/26)

Maximum flows in networks (3/28)

Applications of the Max-Flow/Min-Cut Theorem; Dilworth's Theorem (3/31)

Dilworth's Theorem; perfect graphs; the Greene-Kleitman Theorem (4/2)

Counting group orbits with Polyá theory (4/4)

Representation theory: example, isomorphisms and homomorphisms (4/7)

Maschke's Theorem; characters (4/9)

Operations on characters; the scalar product on class functions (4/11)

Schur's Lemma; orthonormality; computing character tables (4/14)

Proof that the irreducible characters span; characters of abelian groups (4/16)

Characters of the symmetric group (4/18)

Restricted and induced representations (4/21)

Monomial, elementary and homogeneous symmetric functions (4/23)

Power-sum and Schur symmetric functions; proof of basishood (4/25)

The involution ω; a lot of identities; the Hall inner product (4/28)

The Robinson-Schensted-Knuth correspondence, and some consequences (4/30)

Frobenius characteristic; Murnaghan-Nakayama Rule; hook-length formula (5/2)

Also, for reference, here is a list of notation used in these notes (last updated 4/30).

Each student enrolled in Math 796 will have the choice of taking a comprehensive final exam or doing a final project. The final project will consist of reading a research paper or book chapter and giving a short (20-25 minute) presentation to the class. The presentations will take place during the last week of classes (May 5 and 7).

According to the KU Registrar, the final exam is scheduled for Thursday May 15 from 10:30 AM - 1:00 PM, presumably in Snow 408.

All the books in the list below can be perused in Jeremy's office. The official textbook is #1 in the list below; however, you may want to substitute #3, whose material is a bit closer to what will be covered in the class. (All the homework assignments will be self-contained.) You should definitely obtain #4 and #5, which are free downloads.

- R.P. Stanley,
*Enumerative Combinatorics, volume 1*(Cambridge, 1997)

(Enumeration; posets and lattices; generating functions)

Amazon | Google Books - R.P. Stanley,
*Enumerative Combinatorics, volume 2*(Cambridge, 1999)

(More enumeration, including exponential generating functions; symmetric functions)

Amazon | Google Books - M. Aigner,
*Combinatorial Theory*(Springer, 1997)

(Enumeration; posets, lattices, and matroids)

Amazon | Google Books - R.P. Stanley,
*Hyperplane Arrangements*(lecture notes available free online) - A. Schrijver,
*A Course in Combinatorial Optimization*(lecture notes available free online) - T. Brylawski and J. Oxley,
*The Tutte polynomial and its applications*, Chapter 6 of*Matroid applications*, N. White, ed. (Cambridge Univ. Press, 1992) - B.
Sagan,
*The Symmetric Group, 2nd edn.*(Springer, 2001)

- Writing in the Sciences (UNC Chapel Hill Writing Center)
*A Guide to Writing Mathematics*and Mathematical Writing Checklist (Prof. Kevin Lee, Purdue)

- Jeremy's home page
- KU Mathematics Department
- KU Registrar
- KU Bookstore
- KU policies on academic honesty
- KU Office of Disability Resources

- Get Acrobat Reader (free software, necessary to read PDF files on this page)

Last updated Fri 5/2/08