| | | Action on k-subsets |
Further actions of G which can be derived from GX are the actions of G on the sets
[X choose k]:= {M ÍX | | M | = k },
of k- subsets of X, 1 <= k <= | X | , which are defined as follows:
G ´[X choose k] -> [X choose k] :(g,M) -> bar (g)M= {gm | m ÎM },
The action GX is called k- homogeneous if and only if the corresponding action of G on [X choose k] is transitive. An obvious example is the natural action of SX on X, it is k-homogeneous for k <= | X | .
| harald.fripertinger "at" uni-graz.at | http://www-ang.kfunigraz.ac.at/~fripert/ | UNI-Graz | Institut für Mathematik | UNI-Bayreuth | Lehrstuhl II für Mathematik |
| | | Action on k-subsets |