Topics in Algebraic Combinatorics (2024)

Algebraic combinatorics is the field that uses algebraic techniques (mostly linear algebra and group
theory) to study combinatorial problems, or combinatorial techniques (generating functions, counting
techniques) to study algebraic problems. In this course, we will cover several classical topics and learn
useful techniques from both fields.

1. Walks in graphs
2. Generating functions
3. Young tableaux
4. Representations of the symmetric group
5. Symmetric functions
6. Posets
7. Matroids (if time permits)