Some example programs Orbit-enumeration in SYMMETRICA Substitutions into cycle indices Some further cycle index routines

Some further cycle index routines

There is a natural imbedding of a group G acting on the set {1,...,n} into G acting on {1,...,n+1}. (n+1 is a fixed point of each g∈ G). The cycle index of this induced group action can be computed by   
INT zykelind_inc(a,b)       OP a,b;
INT zykelind_inc_apply(a)   OP a;
In the first case a is the cycle index of G on {1,...,n} and b is the cycle index of the induced action. In the second case the induced cycle index from a is computed and then a is replaced by this new cycle index.

The inverse operations to these are  

INT zykelind_dec(a,b)       OP a,b;
INT zykelind_dec_apply(a)   OP a;
When applying these two routines one has to take care that each element of the acting group has at least one fixed point (i.e. it must be granted that a1(g)>0 in the cycle of each g∈ G).
harald.fripertinger "at" uni-graz.at, May 26, 2011

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