Detailed information 
Original study plan 
Master's programme Computer Mathematics 2020W 
Objectives 
Fundamental methods of Algebraic Combinatorics
with special emphasis on the concept of group action.

Subject 
Fundamental objects of Enumerative Combinatorics are
labeled and unlabeled structures; for example, labeled
and unlabeled trees or graphs. Usually the unlabeled
feature is induced by underlying symmetries which,
in proper mathematical specification, are made
explicit by using the concept of group action.
The action of groups on sets was introduced as a
general mathematical paradigm by Felix Klein in
his Erlangen Program published in 1872. Wikipedia:
"The longterm effects of the Erlangen Program can be
seen all over pure mathematics [...] using groups
of symmetry has become standard in physics."
The course introduces to this fundamental mathematical
concept along combinatorial problems like: In how
many different ways can one color a cube using three
different colors for its faces? Applications like
counting chemical isomers use Polya theory which
connects groups to other algebraic objects such
as multivariate polynomials and generating functions.

Criteria for evaluation 
Depending on the number of participants: oral or written examination at the end of the semester

Methods 
Blackboard lectures; distribution of "home works", which
are dealt with in the exercises. Use of computer algebra
systems like Mathematica or Sage.

Language 
English 
Study material 
Textbooks like "Applied Finite Group Actions" by Adalbert Kerber.

Changing subject? 
No 
Corresponding lecture 
404ALMAVAKOV18 or TMCPAVOAKOM: VL Algorithmische Kombinatorik (3 ECTS)
