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@kfunigraz.ac.at,
last changed: August 28, 2001
