Algorithmische Kombinatorik
Topic outline

Di, 12:0013:30 Uhr, HS 14, 1st lecture: 9.3.2010
Enumerative Combinatorics is divided in to two subfields: (a) Counting Theory (yields counting formulae, e.g. complicated formed Summations) and (b) Formel Manipulation Techniques (e.g. simplification of sums of binomial coefficients).This lecture is mainly devoted to Counting theory; the second subfield is treated in the lecture "Analytic Combinatorics".
The first part of the lecture introduces to basic combinatorial sequences like binomial coefficients, partition numbers, or Stirling numbers.
The main part of the lecture is devoted to the concept of group actions. This fundamental concept, connecting algebra with combinatorics, can be viewed as the basis of Polya's counting theory. Typical applications, for instance, concern different colorings of the cube, or determining the total number of molecular graphs of a certain type (e.g., alcohols).
Literature:
A. Kerber: "Finite Group Actions",
D. Stanton and D. White: "Constructive Combinatorics",
S. Skiena, "Implementing Discrete Mathematics (Combinatorics
and Graph Theory with Mathematica)", and others.Requirements: Active knowledge from "Analysis I" and "Lineare Algebra I and II". In addition, parts of the lecture "Computer Algebra I" would be helpful; but this is not an absolutely necessary requirement.
