Dear Hebert, dear GAP Forum,
GAP 4.4.12 already has the non-documented function "CycleIndex"
which you may use. It will become documented in the next release
of GAP 4.5 as follows:
CycleIndex( g, Omega[, act] )
CycleIndex( G, Omega[, act] )
The cycle index of a permutation g acting on Omega is defined as
z(g) = s_1^{c_1} s_2^{c_2} cdots s_n^{c_n}
where c_k is the number of k-cycles in the cycle decomposition
of g and the s_i are indeterminates.
The cycle index of a group G is defined as
Z(G) = ( sum_{g in G} z(g) ) / |G| .
The indeterminates used by CycleIndex are the indeterminates 1 to n
over the rationals.
gap> g:=TransitiveGroup(6,8);
S_4(6c) = 1/2[2^3]S(3)
gap> CycleIndex(g);
1/24*x_1^6+1/8*x_1^2*x_2^2+1/4*x_1^2*x_4+1/4*x_2^3+1/3*x_3^2
Hope this helps,
Alexander
On 19 Dec 2010, at 12:22, Hebert Pérez-Rosés wrote:
> Dear all,
>
> Does anybody have a GAP function to compute the cycle index of a permutation
> group, and perform Polya enumeration?
>
> Best regards,
>
> Hebert Perez-Roses
> The University of Newcastle, Australia
_______________________________________________
Forum mailing list
Forum@mail.gap-system.org
http://mail.gap-system.org/mailman/listinfo/forum
