Some example programs |

**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*C*and then for_{n}*1£i£m*the variable*x*is replaced by_{i}*1+z*.^{i} **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*C*and_{n},D_{n},A_{n}*S*and then each_{n}*x*is replaced by_{i}*å*._{j=1}^{m}z_{j}^{i} **ex30.c**- asks for two INTEGERS
*k,q*and computes the cycle index of*GL*, the order of_{k}(q)*GL*and the number of monic irreducible polynomials of degree_{k}(q)*k*over*GF(q)*. **ex31.c**- computes the 3-dimensional cycle index of the group of all
rotations of the cube. Then 3 INTEGERS
*n*must be input and the number of different colourings of the cube, where the vertices can be coloured with_{1},n_{2},n_{3}*n*colons, the edges with_{1}*n*colours and the faces with_{2}*n*colours, is computed._{3} **ex32.c**- asks for an INTEGER
*n*computes the cycle index of*S*and of the induced actions on the set of all_{n}*2*-sets, all*k*-subsets and on the power-set. **ex33.c**- asks for an INTEGER
*n*computes the cycle index of*S*and of the induced actions on pairs, and_{n}*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*S*and_{n}*S*._{m} **ex36.c**- asks for an INTEGER
*n*and computes the number of classes of bijective functions on*{1,...,n}*, where*D*acts both on the domain and the range. Then it asks for another INTEGER_{n}*m*, and computes the Redfield cup and cap product of*m*copies of*D*._{n}

harald.fripertinger@kfunigraz.ac.at,

last changed: November 19, 2001

Some example programs |