| | | **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 *a*_{1}(g)>0 in the cycle of each *gÎG*).

harald.fripertinger@kfunigraz.ac.at,

last changed: November 19, 2001

| | | **Some further cycle index routines** |