| | | **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** |