   Some basic cycle index formulae

#### Some basic cycle index formulae

There exist some basic routines in order to compute the cycle indices of the natural group actions of cyclic, dihedral, alternating and symmetric groups in SYMMETRICA.

These are the routines

```INT zykelind_Cn(a,b)    OP a,b;
INT zykelind_Dn(a,b)    OP a,b;
INT zykelind_An(a,b)    OP a,b;
INT zykelind_Sn(a,b)    OP a,b;
INT zykelind_In(a,b)    OP a,b;
```
As their names imply one can compute the cycle indices of the natural actions of the cyclic group `Cn`, the dihedral group `Dn`, the alternating group `An`, the symmetric group `Sn` and the trivial group consisting of the identity only `In` respectively. In all these cases `a` is the degree of the permutation group (i.e. the number of elements of the set which the group is acting on). `b` is the computed cycle index. `a` and `b` must be different.

There is another routine called

```INT zykelind_arb(a,b)    OP a,b;
```
which computes the cycle index of an arbitrary permutation group given by a set of generators. In this situation `a` is a VECTOR object, and each entry of `a` is a PERMUTATION object (a generator of the acting group) all of the same length. Again `b` is the computed cycle index. `a` and `b` must be different.
harald.fripertinger@kfunigraz.ac.at,
last changed: November 19, 2001   Some basic cycle index formulae