group(deprecated)/SnConjugates - Maple Help

group(deprecated)

 SnConjugates
 find the number of group elements with a given cycle type

 Calling Sequence SnConjugates(pg, perm) SnConjugates(pg, part)

Parameters

 pg - permutation group perm - permutation in disjoint cycle notation part - partition of the degree of pg

Description

 • Important: The group package has been deprecated. Use the superseding package GroupTheory instead.
 • The cycle type of a permutation refers to its structure.  It can be specified by either a sample permutation with the required cycle type or by a partition of the degree.  For example, the permutation $\left[\left[1,2\right],\left[3,4\right],\left[5,6,7\right]\right]$ and the partition $\left[2,2,3\right]$ refer to the same cycle type.
 • The elements with the same cycle type are conjugates under the action of Sn, where $n$ is the degree of pg and Sn the symmetric group on $\left\{1,...,n\right\}$.
 • If perm is used, the function returns the number of elements of pg that have the same cycle type as perm. Only the structure of perm is considered.
 • If part is used, the function returns the number of elements of pg that have the cycle type described by part.
 • The command with(group,SnConjugates) allows the use of the abbreviated form of this command.

Examples

Important: The group package has been deprecated. Use the superseding package GroupTheory instead.

 > $\mathrm{with}\left(\mathrm{group}\right):$
 > $\mathrm{pg}≔\mathrm{permgroup}\left(4,\left\{\left[\left[1,4\right]\right],\left[\left[1,2\right],\left[3,4\right]\right]\right\}\right):$
 > $\mathrm{SnConjugates}\left(\mathrm{pg},\left[\left[1,2\right],\left[3,4\right]\right]\right)$
 ${3}$ (1)
 > $\mathrm{SnConjugates}\left(\mathrm{pg},\left[2,2\right]\right)$
 ${3}$ (2)
 > $\mathrm{SnConjugates}\left(\mathrm{pg},\left[\left[1,2,3\right]\right]\right)$
 ${0}$ (3)
 > $\mathrm{SnConjugates}\left(\mathrm{pg},\left[3\right]\right)$
 ${0}$ (4)