Combinatorics

General Information

Instructor: Rainer Sinn
Office: Raum A533
Time and Place: Monday, 9:15 to 11:45 in A 314

Combinatorics, the art of counting, is a field with many different branches, topics, methods, questions, and connections. So we have to pick one for this course. The main focus will be on Stanley-Reisner theory, a part of combinatorial commutative algebra. We will see simplicial complexes and connections of counting to (simplicial) topology and the algebraic properties of monomial ideals.
Prior knowledge in abstract algebra is sufficient. Basics in commutative algebra or algebraic topology could be helpful but are not necessary.

Materials

You will find materials for the course mainly on this website.

Lecture notes

Week 1: Generating Functions
Week 2: Monomial ideals and algebraic operations
Week 3: Recap commutative algebra

Sources

Here is a list of useful references that we will use throughout the course.

Herzog, Hibi: Monomial Ideals (Springer 2011)
Miller, Sturmfels: Combinatorial Commutative Algebra (Springer 2005)
Aigner: A Course in Enumeration (Springer 2007)

Exercises

The course will run until the end of term (last class on 1. July).