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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 "at" uni-graz.at, May 26,
2011
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Some basic
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