group[SnConjugates] - find the number of group elements with a given cycle type
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Calling Sequence
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SnConjugates(pg, perm)
SnConjugates(pg, part)
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Parameters
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pg
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permutation group
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perm
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permutation in disjoint cycle notation
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part
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partition of the degree of pg
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Description
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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 and the partition refer to the same cycle type.
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The elements with the same cycle type are conjugates under the action of Sn, where is the degree of pg and Sn the symmetric group on .
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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.
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If part is used, the function returns the number of elements of pg that have the cycle type described by part.
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The command with(group,SnConjugates) allows the use of the abbreviated form of this command.
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Examples
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