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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.

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