250059 VO Combinatorics (2023S)

Prüfungstermine

Lehrende

• Christian Krattenthaler

Termine (iCal) - nächster Termin ist mit N markiert

Combinatorics, in its simplest form, deals with the enumeration of
elements of a finite set. The most frequent basic combinatorial objects
are permutations, rearrangements, lattice paths, trees and graphs.
The appeal of combinatorics comes from the fact that there is no uniform
approach for the treatment of the different problems, but many different
methods, each of which providing a conceptual approach to a particular
type of problem, respectively shedding light on these problems from different
angles. The fact that there are no limitations on imagination in
combinatorics has given a boost to this area in the past.
In particular, the interrelations to other areas, such as theory of
finite groups, representation theory, commutative algebra, algebraic
geometry, computer science, and statistical physics, became more and more
important.
This course will build on the material of the course
"Diskrete Mathematik". Some topics from there will be treated here
in a more profound manner, and there will be new topics,
to be precise:
1. Combinatorial structures and their generating functions
2. P\'olya theory and the enumeration of objects with symmetries
3. Combinatorial theory of partially ordered sets
4. Methods for asymptotic enumeration

Reading list:

Lecture notes are available at
https://www.mat.univie.ac.at/~mfulmek/scripts/KOMBI/skriptum.pdf .

Books to be recommended are:
P. J. Cameron, "Combinatorics", Cambridge University Press, 1994.
P. Flajolet, R. Sedgewick, "Analytic Combinatorics", Cambridge
University Press, 2009.
R. P. Stanley, "Enumerative Combinatorics", Vol. 1, Wadsworth \&
Brooks/Cole, 1986.
D. Stanton und D. White, "Constructive Combinatorics",
Springer-Verlag, 1986.