#
Monday Lecture and Colloquium

**Monday, June 23, 2008 **

Freie Universität Berlin

Institut für Informatik

Takustr. 9,

room 005

** Lecture - 14:15**

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Michael Drmota (TU Wien)

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Generating Functions and Central Limit Theorems

*Abstract:*

Many interesting combinatorial objects can be "counted"
with help of generating functions, for example, set and integer
partitions, several classes of trees and also maps and planar
graphs. With help of bi- resp. multivariate generating functions
it is also very convenient to encode the distribution of specific
parameters. The problem is then to determine the "typical behaviour"
of a parameter if the size of the object of interst goes to infinity.
Actually it turns out that many parameters of interest (e.g. the number
of edges in planar graphs with n vertices) satisfy a central limit theroem.

During the last 10-15 year there has been much progress in
systematizing probabilistic limiting results in combinatorial structures
that can be studied with help of generating functions.
The purpose of this talk is to present a general result in this direction,
when the corresponding generating function(s) satisfy a (system of)
functional equation(s).

As applications we study the number of occurances of patterns
in random trees and the degree distribution in random planar graphs.

**Colloquium - 16:00**

### cancelled

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*Abstract:*

Letzte Aktualisierung:
16.06.2008