In dem regelmäßig stattfindenden Oberseminar tragen Gäste aus aller Welt über Forschungsarbeiten zu Themen vor, die mit der Arbeit von CeVis und MeVis in Verbindung stehen, und Mitarbeiter von CeVis und MeVis präsentieren ihre neusten Ergebnisse.

## C(M)eVis-Oberseminar am 6.12.2000

Datum: Mittwoch, der 6.12.2000
Zeit: 11.00 Uhr s.t.
Ort: Seminarraum Mandelbrot
Referent: Prof. Dr. Andre Barbe (Katholieke Universiteit Leuven, Belgien)
Generalized decimation invariant sequences

A sequence is called decimation invariant (DI) when certain regularly constructed subsequences (so-called decimations) equal the original sequence. The DI-sequences that will be considered are $N$-dimensional sequences $f:\ \Z^N\rightarrow \N$, the decimations of which are defined by an expanding map $H:\ \Z^N \rightarrow \Z^N$ and a corresponding residue set $W$. They satisfy the condition

f(Hs+w)=f(s)

for all $s \in \Z^N$ and all $w \in W$ . They are a generalization of certain one-and two-dimensional DI-sequences that have been studied before and where $H$ and $W$ had naturally" simple forms. It will be shown how solutions for this equation can be obtained. An overview of the most common morphological characteristics of DI-sequences will be given. Periodic solutions seem to form a special class. Conditions for possible periodicity of the solutions will be derived.

A. Rodenhausen, 6.11.2000