CentralizerSize on IntegerPartition
The size of the centralizer of a permutation with these cycle lengths: the product of the parts times the product of the factorials of the multiplicities.
Called as CombinatorialStat(x, "CentralizerSize"). The head's page has its examples.
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Distribution
Over IntegerPartitions at each size, tallied here in your browser; sizes past 30 are not offered.
FindStat St000184
The size of the centralizer of any permutation of given cycle type.
| Object | Value |
|---|---|
[] | 1 |
[1] | 1 |
[2] | 2 |
[3] | 3 |
[4] | 4 |
[5] | 5 |
[6] | 6 |
[7] | 7 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000184 has the rest.