 |  |  | 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 GX on an n-set
by a similar action of a permutation group H£Sn 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 C60
[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 |