 |  |  | Some further cycle index routines |
Some further cycle index routines
There is a natural imbedding of a group G acting on the set
{1,...,n} into G acting on {1,...,n+1} .
(n+1 is a fixed point of each gÎG).
The cycle index of this induced group action can be computed by
INT zykelind_inc(a,b) OP a,b;
INT zykelind_inc_apply(a) OP a;
In the first case a is the cycle index of G on
{1,...,n} and b is the cycle index of the induced action.
In the second case the induced cycle index from a is computed
and then a is replaced by this new cycle index.
The inverse operations to these are
INT zykelind_dec(a,b) OP a,b;
INT zykelind_dec_apply(a) OP a;
When applying these two routines one has to take care that each element
of the acting group has at least one fixed point (i.e. it must be
granted that a1(g)>0 in the cycle of each gÎG).
harald.fripertinger@kfunigraz.ac.at,
last changed: November 19, 2001
| | | Some further cycle index routines |