| | | **Orbit-construction in SYMMETRICA** |

### Orbit-construction in SYMMETRICA

Now let me describe some procedures for computing
complete lists
(so called *transversals*)
of *standard representatives* for a given group action.
For doing this it is convenient to replace an arbitrary group
action _{G}X on an *n*-set
by a similar action of a permutation group *H£S*_{n} on the set *{1,...,n} *.
Then the smallest element of an orbit *w* is considered to
be the standard representative of *w*.
The idea for these routines is the following. Input a permutation group
and a set, where this group is acting on.
The program then computes a list of all orbit representatives.
Such algorithms were used to determine all graphs on *k* points
[11][10],
all different resonance structures of the fullerene C_{60}
[7] or all *k*-motives in music theory
[4][3].

At first it is described how to input permutation groups,
then the various group actions are discussed.

harald.fripertinger@kfunigraz.ac.at,

last changed: November 19, 2001

| | | **Orbit-construction in SYMMETRICA** |