Processing math: 100%

Identifier
Values
[1] => [[1],[]] => 1
[2] => [[2],[]] => 2
[1,1] => [[1,1],[]] => 1
[3] => [[3],[]] => 3
[2,1] => [[2,1],[]] => 1
[1,1,1] => [[1,1,1],[]] => 3
[4] => [[4],[]] => 4
[3,1] => [[3,1],[]] => 1
[2,2] => [[2,2],[]] => 4
[2,1,1] => [[2,1,1],[]] => 1
[1,1,1,1] => [[1,1,1,1],[]] => 2
[5] => [[5],[]] => 5
[4,1] => [[4,1],[]] => 1
[3,2] => [[3,2],[]] => 5
[3,1,1] => [[3,1,1],[]] => 5
[2,2,1] => [[2,2,1],[]] => 5
[2,1,1,1] => [[2,1,1,1],[]] => 1
[1,1,1,1,1] => [[1,1,1,1,1],[]] => 5
[6] => [[6],[]] => 6
[5,1] => [[5,1],[]] => 1
[4,2] => [[4,2],[]] => 6
[4,1,1] => [[4,1,1],[]] => 3
[3,3] => [[3,3],[]] => 3
[3,2,1] => [[3,2,1],[]] => 2
[3,1,1,1] => [[3,1,1,1],[]] => 3
[2,2,2] => [[2,2,2],[]] => 6
[2,2,1,1] => [[2,2,1,1],[]] => 3
[2,1,1,1,1] => [[2,1,1,1,1],[]] => 2
[1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => 3
[7] => [[7],[]] => 7
[6,1] => [[6,1],[]] => 1
[5,2] => [[5,2],[]] => 7
[5,1,1] => [[5,1,1],[]] => 7
[4,3] => [[4,3],[]] => 7
[4,2,1] => [[4,2,1],[]] => 7
[4,1,1,1] => [[4,1,1,1],[]] => 1
[3,3,1] => [[3,3,1],[]] => 7
[3,2,2] => [[3,2,2],[]] => 7
[3,2,1,1] => [[3,2,1,1],[]] => 7
[3,1,1,1,1] => [[3,1,1,1,1],[]] => 7
[2,2,2,1] => [[2,2,2,1],[]] => 7
[2,2,1,1,1] => [[2,2,1,1,1],[]] => 7
[2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => 1
[1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => 7
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Description
The cyclic permutation representation number of a skew partition.
This is the size of the largest cyclic group C such that the fake degree is the character of a permutation representation of C.
See St001527The cyclic permutation representation number of an integer partition. for the restriction of this statistic to integer partitions.
Map
to skew partition
Description
The partition regarded as a skew partition.