Dear Forum,

Pamb <pamb@mathematik.uni-wuerzburg.de> wrote:

I have a set S with 30 elements, together with a symmetric binary relation R, which
holds between some of the elements of S. I would like to find out all the
permutations of S which preserve the relation R, in the following precise sense
f: S to S, f bijection satisfying "a R b if and only if f(a) R f(b)".

Is there any program in GAP that would allow me to do that?

The GAP share package GRAPE can do this using nauty (so GRAPE must be
fully installed on a UNIX system).

First, use the GRAPE function `Graph' to define a GRAPE graph with
vertex-set S and with [a,b] an edge iff aRb. See the documentation.
For example, after defining S and R appropriately, you will enter
something like:
gamma:=Graph(Group(()),S,function(x,g) return x; end,R,true);

Then the permutations you require form a group, which is the
automorphism group of your graph gamma. This group is calculated by
AutGroupGraph(gamma);

-Leonard Soicher.