## Proposed staff

It is planned to employ Dr. H. Fripertinger for three years in this
research project since he is working in the field of algebraic
combinatorics for many year. He started to investigate and implement
algorithms for the construction of orbit representatives under finite group
actions in his PhD thesis [17][16]. Since that time a very productive
cooperation together with Prof. A. Kerber from Lehrstuhl II at the
university in Bayreuth developed. During the last two and a half years
H. Fripertinger was working in the FWF-project *Konstruktion endlicher
Strukturen* P10189 - PHY. Many results obtained in this project can be
seen as a foundation for this new project:
- In the field of
*coding theory* the following articles
[23][19][18][21] are dealing with
enumeration of linear codes. In [13] it is demonstrated how to
enumerate, construct and generate block codes uniformly at random.
The concept of block codes generalizes the symmetry types of boolean
functions or switching functions and block codes can be used for the
construction of Post-functions.
- The
*cycle indices* for the natural actions of linear, affine and
projective linear groups (needed for the enumeration of the isometry classes
of linear codes) were determined in [12].
- There are some connections between
*species* theory and the
enumeration of endofunctions of given cycle type [24].
- In [20][22] the cycle indices of the symmetry groups of various
*fullerenes* were determined.
- Some combinatorial problems arising from
*musical theory* were
discussed in [14].
- In cooperation with M. Wild a
*regularity test*
for binary matrix matroids was developed and implemented.
- In SYMMETRICA H. Fripertinger implemented most of the cycle index
routines and wrote some programs for computing generating functions,
type counting functions and cycle index series from species theory.

H. Fripertinger presented these results at the AAECC-11 in Paris in July
1995, at the IX. Mathematikertreffen Zagreb-Graz, in Motovun in June
1995, at Groups in
Action in Thurnau '96 in October 1996
and at several meetings of the Séminaire
Lotharingien de Combinatoire.
This proposed contract of employment will be necessary to guarantee the
collaboration with H. Fripertinger for the next years.
It leads to the following charges per annum:

1 contract of employment AS 492.000,-

harald.fripertinger@kfunigraz.ac.at,

last changed: January 23, 2001