Syllabus

Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session

Prerequisites

Algebra I (18.701) or Modern Algebra (18.703)

Course Content

This is an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected, but I will assume a familiarity with linear algebra and finite groups. We will cover a number of topics chosen to show the beauty and power of techniques in algebraic combinatorics. Rigorous mathematical proofs are expected.

• Rational generating functions and Recurrence relations
• Walks in graphs and the Radon transform
• Adjacency and Laplacian matrices of graphs
• Introduction to Posets and Sperner's theorem
• Partitions and Euler's Pentagonal theorem
• Young diagrams and q-binomial coefficients
• Young Tableaux and introduction to Schur functions
• Robinson-Schensted-Knuth algorithm and applications
• Polya theory and group actions on boolean algebras
• Matrix Tree theorem, Spanning trees, and Eulerian digraphs

Recommended Texts

Stanley, Richard P. Enumerative Combinatorics. Vol. 1. Cambridge, UK: Cambridge University Press, 1997. ISBN: 9780521553094.

———. Enumerative Combinatorics. Vol. 2. Cambridge, UK: Cambridge University Press, 2001. ISBN: 9780521789875.

"Topics in Algebraic Combinatorics." by Richard Stanley
Notes available online (PDF).

Requirements

Homework: Homework will be assigned and collected in class, typically every week. Your lowest homework score will be dropped.

Exams: There will be two in-class quizzes during the semester.

Research Project: You will be expected to write a 5-10 page expository paper on a topic in algebraic combinatorics related to the course material.

Participation: Participation in class is encouraged. Please feel free to stop me and ask questions. Otherwise, I might stop and ask you questions.

Grading