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SpechtModule :: cardinalityOfConjugacyClass(Partition)

cardinalityOfConjugacyClass(Partition) -- the size of the conjugacy classes of S_n

Synopsis

Description

The formula for this classes is obtained by the Orbit-Stabilizer lemma applied for Sn with the action of conjugation.

For a partition p this formula is n!/(∏ii )!iλi, where λi denotes the number of parts in p that are equal to i.

i1 : p1 = new Partition from {3,2,1}

o1 = Partition{3, 2, 1}

o1 : Partition
i2 : cardinalityOfConjugacyClass p1

o2 = 120
i3 : p2 = new Partition from {1,1,1,1,1}

o3 = Partition{1, 1, 1, 1, 1}

o3 : Partition
i4 : cardinalityOfConjugacyClass p2

o4 = 1