| Detailed information |
| Original study plan |
Master's programme Computational Mathematics 2023W |
| Objectives |
Fundamental methods of Algebraic Combinatorics with special emphasis on the concept of group action.
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| 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 long-term 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.
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| Criteria for evaluation |
Depending on the number of participants: oral or written examination at the end of the semester
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| 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.
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| Changing subject? |
No |
| Corresponding lecture |
TMCPAVOAKOM: VL Algorithmische Kombinatorik (3 ECTS)
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| Earlier variants |
They also cover the requirements of the curriculum (from - to)
404ANDMACOV20: VL Algebraic combinatorics (2020W-2023S)
404ALMAVAKOV18: VL Algebraic combinatorics (2018W-2020S)
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