Applications Finite group actions Orbit-enumeration in SYMMETRICA 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 ω is considered to be the standard representative of ω.

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 "at" uni-graz.at, May 26, 2011

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