Orbit-enumeration in SYMMETRICASome further cycle index routinesSome example programs

Some example programs

There are some example programs illustrating the usage of these routines:
ex12.c
asks for an INTEGER and computes the cycle indices of the corresponding cyclic, dihedral, alternating and symmetric groups.
ex13.c
asks for two INTEGERS n and m, computes the cycle index of Cn and then for 1£i£m the variable xi is replaced by 1+zi.
ex14.c
asks for a VECTOR object; each entry of this object must be a PERMUTATION object (all of the same length). These are the generators of a group and the cycle index of this group is computed.
ex20.c
asks for two INTEGERS n and m, computes the cycle indices of Cn,Dn,An and Sn and then each xi is replaced by åj=1m zji.
ex30.c
asks for two INTEGERS k,q and computes the cycle index of GLk(q), the order of GLk(q) and the number of monic irreducible polynomials of degree k over GF(q).
ex31.c
computes the 3-dimensional cycle index of the group of all rotations of the cube. Then 3 INTEGERS n1,n2,n3 must be input and the number of different colourings of the cube, where the vertices can be coloured with n1 colons, the edges with n2 colours and the faces with n3 colours, is computed.
ex32.c
asks for an INTEGER n computes the cycle index of Sn and of the induced actions on the set of all 2-sets, all k-subsets and on the power-set.
ex33.c
asks for an INTEGER n computes the cycle index of Sn and of the induced actions on pairs, and k-tuples.
ex34.c
asks for an INTEGER n and computes the number of classes of linear graphs, directed graphs (with and without loops and with loops and edges distinguished), oriented graphs and tournaments and superpositions of a linear and a directed graph with n vertices.
ex35.c
asks for two INTEGER n,m computes the cycle indices of of the direct sum, the direct product, and the wreath product (acting on {1,...,n} ´{1,...,m} ) of Sn and Sm.
ex36.c
asks for an INTEGER n and computes the number of classes of bijective functions on {1,...,n} , where Dn acts both on the domain and the range. Then it asks for another INTEGER m, and computes the Redfield cup and cap product of m copies of Dn.

harald.fripertinger@kfunigraz.ac.at,
last changed: November 19, 2001

Orbit-enumeration in SYMMETRICASome further cycle index routinesSome example programs