Abstract: A relational structure A with a countable universe is
defined to be homogeneous iff every finite partial isomorphism of A
can be extended to an automorphism of A. The structure A may be
endowed with the discrete topology, then the automorphism group of A
becomes a topological group (with the suitable topological power of
the discrete topology on A).
An automorphism of A is defined to be generic iff its conjugacy class
(in the group theoretic sense) is dense in the topologal sense.
We will present sufficient conditions implying the existence of generic
automorphisms of certain homogeneous structures. Connections with
finite combinatorics will also be discussed.