Algebraic Combinatorics
The lecture takes place on Tuesdays, 12:00-13:30 in HS14 starting October 3, 2023. The lecture will be held in English. There are exercises attached to the lecture that are not mandatory but highly recommended. The exercises will be held by
Koustav Banerjee. Currently they are set to be held on Tuesdays, 13:45-14:30 in HS14, but the times are open for discussion. The details of the exercises will be organized in the first lecture.
Enumerative Combinatorics is divided in two subfields: (i) Counting Theory and (ii) Formal Manipulation Techniques. This lecture is mainly devoted to Counting Theory; the other subfield is treated in the lecture Algorithmic Combinatorics.
In this lecture basic combinatorical sequences such as binomial coefficients, Stirling numbers, or partition numbers are introduced as well as the concept of group actions. The latter is a fundamental concept that connects algebra with combinatorics.
Literature:
- R. P. Stanley: Algebraic Combinatorics - Walks, Trees, Tableaux and More
- R. P. Stanley: Enumerative Combinatorics: Volume 2
- D. Stanton and D. White: Constructive Combinatorics
- S. Skiena: Implementing Discrete Mathematics (Combinatorics and Graph Theory with Mathemtica)"
Requirements: Basic knowledge from analysis and linear algebra.
Veronika Pillwein
