- FindStat

Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St001527

Mapping

Mp00027: Dyck paths —to partition⟶ Integer partitions
St001527: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

[1,0,1,0]
 => [1]
 => 1
[1,0,1,0,1,0]
 => [2,1]
 => 1
[1,0,1,1,0,0]
 => [1,1]
 => 1
[1,1,0,0,1,0]
 => [2]
 => 2
[1,1,0,1,0,0]
 => [1]
 => 1
[1,0,1,0,1,0,1,0]
 => [3,2,1]
 => 2
[1,0,1,0,1,1,0,0]
 => [2,2,1]
 => 5
[1,0,1,1,0,0,1,0]
 => [3,1,1]
 => 5
[1,0,1,1,0,1,0,0]
 => [2,1,1]
 => 1
[1,0,1,1,1,0,0,0]
 => [1,1,1]
 => 3
[1,1,0,0,1,0,1,0]
 => [3,2]
 => 5
[1,1,0,0,1,1,0,0]
 => [2,2]
 => 4
[1,1,0,1,0,0,1,0]
 => [3,1]
 => 1
[1,1,0,1,0,1,0,0]
 => [2,1]
 => 1
[1,1,0,1,1,0,0,0]
 => [1,1]
 => 1
[1,1,1,0,0,0,1,0]
 => [3]
 => 3
[1,1,1,0,0,1,0,0]
 => [2]
 => 2
[1,1,1,0,1,0,0,0]
 => [1]
 => 1
[1,0,1,0,1,0,1,0,1,0]
 => [4,3,2,1]
 => 2
[1,0,1,0,1,0,1,1,0,0]
 => [3,3,2,1]
 => 1
[1,0,1,0,1,1,0,0,1,0]
 => [4,2,2,1]
 => 9
[1,0,1,0,1,1,0,1,0,0]
 => [3,2,2,1]
 => 1
[1,0,1,0,1,1,1,0,0,0]
 => [2,2,2,1]
 => 7
[1,0,1,1,0,0,1,0,1,0]
 => [4,3,1,1]
 => 9
[1,0,1,1,0,0,1,1,0,0]
 => [3,3,1,1]
 => 8
[1,0,1,1,0,1,0,0,1,0]
 => [4,2,1,1]
 => 1
[1,0,1,1,0,1,0,1,0,0]
 => [3,2,1,1]
 => 7
[1,0,1,1,0,1,1,0,0,0]
 => [2,2,1,1]
 => 3
[1,0,1,1,1,0,0,0,1,0]
 => [4,1,1,1]
 => 1
[1,0,1,1,1,0,0,1,0,0]
 => [3,1,1,1]
 => 3
[1,0,1,1,1,0,1,0,0,0]
 => [2,1,1,1]
 => 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => 2
[1,1,0,0,1,0,1,0,1,0]
 => [4,3,2]
 => 1
[1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => 1
[1,1,0,0,1,1,0,0,1,0]
 => [4,2,2]
 => 8
[1,1,0,0,1,1,0,1,0,0]
 => [3,2,2]
 => 7
[1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => 6
[1,1,0,1,0,0,1,0,1,0]
 => [4,3,1]
 => 1
[1,1,0,1,0,0,1,1,0,0]
 => [3,3,1]
 => 7
[1,1,0,1,0,1,0,0,1,0]
 => [4,2,1]
 => 7
[1,1,0,1,0,1,0,1,0,0]
 => [3,2,1]
 => 2
[1,1,0,1,0,1,1,0,0,0]
 => [2,2,1]
 => 5
[1,1,0,1,1,0,0,0,1,0]
 => [4,1,1]
 => 3
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,1]
 => 5
[1,1,0,1,1,0,1,0,0,0]
 => [2,1,1]
 => 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1]
 => 3
[1,1,1,0,0,0,1,0,1,0]
 => [4,3]
 => 7
[1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => 3
[1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => 6
[1,1,1,0,0,1,0,1,0,0]
 => [3,2]
 => 5

Description

The cyclic permutation representation number of an integer partition. This is the size of the largest cyclic group $C$ such that the fake degree is the character of a permutation representation of $C$.

Matching statistic: St001614
(load all 2 compositions to match this statistic)

Mapping

Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
St001614: Skew partitions ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 41%

Values

[1,0,1,0]
 => [1]
 => [[1],[]]
 => 1
[1,0,1,0,1,0]
 => [2,1]
 => [[2,1],[]]
 => 1
[1,0,1,1,0,0]
 => [1,1]
 => [[1,1],[]]
 => 1
[1,1,0,0,1,0]
 => [2]
 => [[2],[]]
 => 2
[1,1,0,1,0,0]
 => [1]
 => [[1],[]]
 => 1
[1,0,1,0,1,0,1,0]
 => [3,2,1]
 => [[3,2,1],[]]
 => 2
[1,0,1,0,1,1,0,0]
 => [2,2,1]
 => [[2,2,1],[]]
 => 5
[1,0,1,1,0,0,1,0]
 => [3,1,1]
 => [[3,1,1],[]]
 => 5
[1,0,1,1,0,1,0,0]
 => [2,1,1]
 => [[2,1,1],[]]
 => 1
[1,0,1,1,1,0,0,0]
 => [1,1,1]
 => [[1,1,1],[]]
 => 3
[1,1,0,0,1,0,1,0]
 => [3,2]
 => [[3,2],[]]
 => 5
[1,1,0,0,1,1,0,0]
 => [2,2]
 => [[2,2],[]]
 => 4
[1,1,0,1,0,0,1,0]
 => [3,1]
 => [[3,1],[]]
 => 1
[1,1,0,1,0,1,0,0]
 => [2,1]
 => [[2,1],[]]
 => 1
[1,1,0,1,1,0,0,0]
 => [1,1]
 => [[1,1],[]]
 => 1
[1,1,1,0,0,0,1,0]
 => [3]
 => [[3],[]]
 => 3
[1,1,1,0,0,1,0,0]
 => [2]
 => [[2],[]]
 => 2
[1,1,1,0,1,0,0,0]
 => [1]
 => [[1],[]]
 => 1
[1,0,1,0,1,0,1,0,1,0]
 => [4,3,2,1]
 => [[4,3,2,1],[]]
 => ? = 2
[1,0,1,0,1,0,1,1,0,0]
 => [3,3,2,1]
 => [[3,3,2,1],[]]
 => ? = 1
[1,0,1,0,1,1,0,0,1,0]
 => [4,2,2,1]
 => [[4,2,2,1],[]]
 => ? = 9
[1,0,1,0,1,1,0,1,0,0]
 => [3,2,2,1]
 => [[3,2,2,1],[]]
 => ? = 1
[1,0,1,0,1,1,1,0,0,0]
 => [2,2,2,1]
 => [[2,2,2,1],[]]
 => 7
[1,0,1,1,0,0,1,0,1,0]
 => [4,3,1,1]
 => [[4,3,1,1],[]]
 => ? = 9
[1,0,1,1,0,0,1,1,0,0]
 => [3,3,1,1]
 => [[3,3,1,1],[]]
 => ? = 8
[1,0,1,1,0,1,0,0,1,0]
 => [4,2,1,1]
 => [[4,2,1,1],[]]
 => ? = 1
[1,0,1,1,0,1,0,1,0,0]
 => [3,2,1,1]
 => [[3,2,1,1],[]]
 => 7
[1,0,1,1,0,1,1,0,0,0]
 => [2,2,1,1]
 => [[2,2,1,1],[]]
 => 3
[1,0,1,1,1,0,0,0,1,0]
 => [4,1,1,1]
 => [[4,1,1,1],[]]
 => 1
[1,0,1,1,1,0,0,1,0,0]
 => [3,1,1,1]
 => [[3,1,1,1],[]]
 => 3
[1,0,1,1,1,0,1,0,0,0]
 => [2,1,1,1]
 => [[2,1,1,1],[]]
 => 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => [[1,1,1,1],[]]
 => 2
[1,1,0,0,1,0,1,0,1,0]
 => [4,3,2]
 => [[4,3,2],[]]
 => ? = 1
[1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => [[3,3,2],[]]
 => ? = 1
[1,1,0,0,1,1,0,0,1,0]
 => [4,2,2]
 => [[4,2,2],[]]
 => ? = 8
[1,1,0,0,1,1,0,1,0,0]
 => [3,2,2]
 => [[3,2,2],[]]
 => 7
[1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => [[2,2,2],[]]
 => 6
[1,1,0,1,0,0,1,0,1,0]
 => [4,3,1]
 => [[4,3,1],[]]
 => ? = 1
[1,1,0,1,0,0,1,1,0,0]
 => [3,3,1]
 => [[3,3,1],[]]
 => 7
[1,1,0,1,0,1,0,0,1,0]
 => [4,2,1]
 => [[4,2,1],[]]
 => 7
[1,1,0,1,0,1,0,1,0,0]
 => [3,2,1]
 => [[3,2,1],[]]
 => 2
[1,1,0,1,0,1,1,0,0,0]
 => [2,2,1]
 => [[2,2,1],[]]
 => 5
[1,1,0,1,1,0,0,0,1,0]
 => [4,1,1]
 => [[4,1,1],[]]
 => 3
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,1]
 => [[3,1,1],[]]
 => 5
[1,1,0,1,1,0,1,0,0,0]
 => [2,1,1]
 => [[2,1,1],[]]
 => 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1]
 => [[1,1,1],[]]
 => 3
[1,1,1,0,0,0,1,0,1,0]
 => [4,3]
 => [[4,3],[]]
 => 7
[1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => [[3,3],[]]
 => 3
[1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => [[4,2],[]]
 => 6
[1,1,1,0,0,1,0,1,0,0]
 => [3,2]
 => [[3,2],[]]
 => 5
[1,1,1,0,0,1,1,0,0,0]
 => [2,2]
 => [[2,2],[]]
 => 4
[1,1,1,0,1,0,0,0,1,0]
 => [4,1]
 => [[4,1],[]]
 => 1
[1,1,1,0,1,0,0,1,0,0]
 => [3,1]
 => [[3,1],[]]
 => 1
[1,1,1,0,1,0,1,0,0,0]
 => [2,1]
 => [[2,1],[]]
 => 1
[1,1,1,0,1,1,0,0,0,0]
 => [1,1]
 => [[1,1],[]]
 => 1
[1,1,1,1,0,0,0,0,1,0]
 => [4]
 => [[4],[]]
 => 4
[1,1,1,1,0,0,0,1,0,0]
 => [3]
 => [[3],[]]
 => 3
[1,1,1,1,0,0,1,0,0,0]
 => [2]
 => [[2],[]]
 => 2
[1,1,1,1,0,1,0,0,0,0]
 => [1]
 => [[1],[]]
 => 1
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [5,4,3,2,1]
 => [[5,4,3,2,1],[]]
 => ? = 3
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [4,4,3,2,1]
 => [[4,4,3,2,1],[]]
 => ? = 14
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [5,3,3,2,1]
 => [[5,3,3,2,1],[]]
 => ? = 14
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [4,3,3,2,1]
 => [[4,3,3,2,1],[]]
 => ? = 13
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [3,3,3,2,1]
 => [[3,3,3,2,1],[]]
 => ? = 4
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [5,4,2,2,1]
 => [[5,4,2,2,1],[]]
 => ? = 2
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [4,4,2,2,1]
 => [[4,4,2,2,1],[]]
 => ? = 13
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [5,3,2,2,1]
 => [[5,3,2,2,1],[]]
 => ? = 13
[1,0,1,0,1,1,0,1,0,1,0,0]
 => [4,3,2,2,1]
 => [[4,3,2,2,1],[]]
 => ? = 3
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [3,3,2,2,1]
 => [[3,3,2,2,1],[]]
 => ? = 11
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [5,2,2,2,1]
 => [[5,2,2,2,1],[]]
 => ? = 4
[1,0,1,0,1,1,1,0,0,1,0,0]
 => [4,2,2,2,1]
 => [[4,2,2,2,1],[]]
 => ? = 11
[1,0,1,0,1,1,1,0,1,0,0,0]
 => [3,2,2,2,1]
 => [[3,2,2,2,1],[]]
 => ? = 2
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [2,2,2,2,1]
 => [[2,2,2,2,1],[]]
 => ? = 1
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,1]
 => [[5,4,3,1,1],[]]
 => ? = 14
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [4,4,3,1,1]
 => [[4,4,3,1,1],[]]
 => ? = 13
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [5,3,3,1,1]
 => [[5,3,3,1,1],[]]
 => ? = 13
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [4,3,3,1,1]
 => [[4,3,3,1,1],[]]
 => ? = 12
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [3,3,3,1,1]
 => [[3,3,3,1,1],[]]
 => ? = 11
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [5,4,2,1,1]
 => [[5,4,2,1,1],[]]
 => ? = 13
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [4,4,2,1,1]
 => [[4,4,2,1,1],[]]
 => ? = 3
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [5,3,2,1,1]
 => [[5,3,2,1,1],[]]
 => ? = 12
[1,0,1,1,0,1,0,1,0,1,0,0]
 => [4,3,2,1,1]
 => [[4,3,2,1,1],[]]
 => ? = 11
[1,0,1,1,0,1,0,1,1,0,0,0]
 => [3,3,2,1,1]
 => [[3,3,2,1,1],[]]
 => ? = 10
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [5,2,2,1,1]
 => [[5,2,2,1,1],[]]
 => ? = 11
[1,0,1,1,0,1,1,0,0,1,0,0]
 => [4,2,2,1,1]
 => [[4,2,2,1,1],[]]
 => ? = 5
[1,0,1,1,0,1,1,0,1,0,0,0]
 => [3,2,2,1,1]
 => [[3,2,2,1,1],[]]
 => ? = 9
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [2,2,2,1,1]
 => [[2,2,2,1,1],[]]
 => ? = 1
[1,0,1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,1,1]
 => [[5,4,1,1,1],[]]
 => ? = 4
[1,0,1,1,1,0,0,0,1,1,0,0]
 => [4,4,1,1,1]
 => [[4,4,1,1,1],[]]
 => ? = 11
[1,0,1,1,1,0,0,1,0,0,1,0]
 => [5,3,1,1,1]
 => [[5,3,1,1,1],[]]
 => ? = 11
[1,0,1,1,1,0,0,1,0,1,0,0]
 => [4,3,1,1,1]
 => [[4,3,1,1,1],[]]
 => ? = 10
[1,0,1,1,1,0,0,1,1,0,0,0]
 => [3,3,1,1,1]
 => [[3,3,1,1,1],[]]
 => ? = 9
[1,0,1,1,1,0,1,0,0,0,1,0]
 => [5,2,1,1,1]
 => [[5,2,1,1,1],[]]
 => ? = 2
[1,0,1,1,1,0,1,0,0,1,0,0]
 => [4,2,1,1,1]
 => [[4,2,1,1,1],[]]
 => ? = 9
[1,0,1,1,1,0,1,0,1,0,0,0]
 => [3,2,1,1,1]
 => [[3,2,1,1,1],[]]
 => ? = 8
[1,0,1,1,1,0,1,1,0,0,0,0]
 => [2,2,1,1,1]
 => [[2,2,1,1,1],[]]
 => 7
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [5,1,1,1,1]
 => [[5,1,1,1,1],[]]
 => ? = 1
[1,0,1,1,1,1,0,0,0,1,0,0]
 => [4,1,1,1,1]
 => [[4,1,1,1,1],[]]
 => ? = 2
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [3,1,1,1,1]
 => [[3,1,1,1,1],[]]
 => 7
[1,1,0,0,1,0,1,0,1,0,1,0]
 => [5,4,3,2]
 => [[5,4,3,2],[]]
 => ? = 14

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 [[St001527]] for the restriction of this statistic to integer partitions.

Matching statistic: St001816

Mapping

Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
St001816: Standard tableaux ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 12%

Values

[1,0,1,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 0 = 1 - 1
[1,0,1,0,1,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 0 = 1 - 1
[1,0,1,1,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 0 = 1 - 1
[1,1,0,0,1,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 1 = 2 - 1
[1,1,0,1,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 0 = 1 - 1
[1,0,1,0,1,0,1,0]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [[1,3,5,7],[2,4,6,8]]
 => ? = 2 - 1
[1,0,1,0,1,1,0,0]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [[1,3,5,6],[2,4,7,8]]
 => ? = 5 - 1
[1,0,1,1,0,0,1,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [[1,3,4,7],[2,5,6,8]]
 => ? = 5 - 1
[1,0,1,1,0,1,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [[1,3,4,6],[2,5,7,8]]
 => ? = 1 - 1
[1,0,1,1,1,0,0,0]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [[1,3,4,5],[2,6,7,8]]
 => ? = 3 - 1
[1,1,0,0,1,0,1,0]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [[1,2,5,7],[3,4,6,8]]
 => ? = 5 - 1
[1,1,0,0,1,1,0,0]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [[1,2,5,6],[3,4,7,8]]
 => ? = 4 - 1
[1,1,0,1,0,0,1,0]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [[1,2,4,7],[3,5,6,8]]
 => ? = 1 - 1
[1,1,0,1,0,1,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 0 = 1 - 1
[1,1,0,1,1,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 0 = 1 - 1
[1,1,1,0,0,0,1,0]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [[1,2,3,7],[4,5,6,8]]
 => ? = 3 - 1
[1,1,1,0,0,1,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 1 = 2 - 1
[1,1,1,0,1,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 0 = 1 - 1
[1,0,1,0,1,0,1,0,1,0]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => [[1,3,5,7,9],[2,4,6,8,10]]
 => ? = 2 - 1
[1,0,1,0,1,0,1,1,0,0]
 => [3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [[1,3,5,7,8],[2,4,6,9,10]]
 => ? = 1 - 1
[1,0,1,0,1,1,0,0,1,0]
 => [4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,0]
 => [[1,3,5,6,9],[2,4,7,8,10]]
 => ? = 9 - 1
[1,0,1,0,1,1,0,1,0,0]
 => [3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [[1,3,5,6,8],[2,4,7,9,10]]
 => ? = 1 - 1
[1,0,1,0,1,1,1,0,0,0]
 => [2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [[1,3,5,6,7],[2,4,8,9,10]]
 => ? = 7 - 1
[1,0,1,1,0,0,1,0,1,0]
 => [4,3,1,1]
 => [1,0,1,1,0,0,1,0,1,0]
 => [[1,3,4,7,9],[2,5,6,8,10]]
 => ? = 9 - 1
[1,0,1,1,0,0,1,1,0,0]
 => [3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0]
 => [[1,3,4,7,8],[2,5,6,9,10]]
 => ? = 8 - 1
[1,0,1,1,0,1,0,0,1,0]
 => [4,2,1,1]
 => [1,0,1,1,0,1,0,0,1,0]
 => [[1,3,4,6,9],[2,5,7,8,10]]
 => ? = 1 - 1
[1,0,1,1,0,1,0,1,0,0]
 => [3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [[1,3,4,6,8],[2,5,7,9,10]]
 => ? = 7 - 1
[1,0,1,1,0,1,1,0,0,0]
 => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [[1,3,4,6,7],[2,5,8,9,10]]
 => ? = 3 - 1
[1,0,1,1,1,0,0,0,1,0]
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [[1,3,4,5,9],[2,6,7,8,10]]
 => ? = 1 - 1
[1,0,1,1,1,0,0,1,0,0]
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 3 - 1
[1,0,1,1,1,0,1,0,0,0]
 => [2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [[1,3,4,5,7],[2,6,8,9,10]]
 => ? = 1 - 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [[1,3,4,5,6],[2,7,8,9,10]]
 => ? = 2 - 1
[1,1,0,0,1,0,1,0,1,0]
 => [4,3,2]
 => [1,1,0,0,1,0,1,0,1,0]
 => [[1,2,5,7,9],[3,4,6,8,10]]
 => ? = 1 - 1
[1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => [1,1,0,0,1,0,1,1,0,0]
 => [[1,2,5,7,8],[3,4,6,9,10]]
 => ? = 1 - 1
[1,1,0,0,1,1,0,0,1,0]
 => [4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [[1,2,5,6,9],[3,4,7,8,10]]
 => ? = 8 - 1
[1,1,0,0,1,1,0,1,0,0]
 => [3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [[1,2,5,6,8],[3,4,7,9,10]]
 => ? = 7 - 1
[1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [[1,2,5,6,7],[3,4,8,9,10]]
 => ? = 6 - 1
[1,1,0,1,0,0,1,0,1,0]
 => [4,3,1]
 => [1,1,0,1,0,0,1,0,1,0]
 => [[1,2,4,7,9],[3,5,6,8,10]]
 => ? = 1 - 1
[1,1,0,1,0,0,1,1,0,0]
 => [3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [[1,2,4,7,8],[3,5,6,9,10]]
 => ? = 7 - 1
[1,1,0,1,0,1,0,0,1,0]
 => [4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [[1,2,4,6,9],[3,5,7,8,10]]
 => ? = 7 - 1
[1,1,0,1,0,1,0,1,0,0]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [[1,3,5,7],[2,4,6,8]]
 => ? = 2 - 1
[1,1,0,1,0,1,1,0,0,0]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [[1,3,5,6],[2,4,7,8]]
 => ? = 5 - 1
[1,1,0,1,1,0,0,0,1,0]
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [[1,2,4,5,9],[3,6,7,8,10]]
 => ? = 3 - 1
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [[1,3,4,7],[2,5,6,8]]
 => ? = 5 - 1
[1,1,0,1,1,0,1,0,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [[1,3,4,6],[2,5,7,8]]
 => ? = 1 - 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [[1,3,4,5],[2,6,7,8]]
 => ? = 3 - 1
[1,1,1,0,0,0,1,0,1,0]
 => [4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [[1,2,3,7,9],[4,5,6,8,10]]
 => ? = 7 - 1
[1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [[1,2,3,7,8],[4,5,6,9,10]]
 => ? = 3 - 1
[1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [[1,2,3,6,9],[4,5,7,8,10]]
 => ? = 6 - 1
[1,1,1,0,0,1,0,1,0,0]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [[1,2,5,7],[3,4,6,8]]
 => ? = 5 - 1
[1,1,1,0,0,1,1,0,0,0]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [[1,2,5,6],[3,4,7,8]]
 => ? = 4 - 1
[1,1,1,0,1,0,0,0,1,0]
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [[1,2,3,5,9],[4,6,7,8,10]]
 => ? = 1 - 1
[1,1,1,0,1,0,0,1,0,0]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [[1,2,4,7],[3,5,6,8]]
 => ? = 1 - 1
[1,1,1,0,1,0,1,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 0 = 1 - 1
[1,1,1,0,1,1,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 0 = 1 - 1
[1,1,1,1,0,0,0,0,1,0]
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [[1,2,3,4,9],[5,6,7,8,10]]
 => ? = 4 - 1
[1,1,1,1,0,0,0,1,0,0]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [[1,2,3,7],[4,5,6,8]]
 => ? = 3 - 1
[1,1,1,1,0,0,1,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 1 = 2 - 1
[1,1,1,1,0,1,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 0 = 1 - 1
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [[1,3,5,7,9,11],[2,4,6,8,10,12]]
 => ? = 3 - 1
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [4,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [[1,3,5,7,9,10],[2,4,6,8,11,12]]
 => ? = 14 - 1
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [5,3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [[1,3,5,7,8,11],[2,4,6,9,10,12]]
 => ? = 14 - 1
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [4,3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [[1,3,5,7,8,10],[2,4,6,9,11,12]]
 => ? = 13 - 1
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 0 = 1 - 1
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 0 = 1 - 1
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 1 = 2 - 1
[1,1,1,1,1,0,1,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 0 = 1 - 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 0 = 1 - 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 0 = 1 - 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 1 = 2 - 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 0 = 1 - 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 0 = 1 - 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 0 = 1 - 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 1 = 2 - 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 0 = 1 - 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 0 = 1 - 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 0 = 1 - 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 1 = 2 - 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 0 = 1 - 1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 0 = 1 - 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 1 = 2 - 1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 0 = 1 - 1
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [[1,2,5],[3,4,6]]
 => 1 = 2 - 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 0 = 1 - 1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [[1,3],[2,4]]
 => 0 = 1 - 1
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 0 = 1 - 1
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [[1,3,5],[2,4,6]]
 => 0 = 1 - 1
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [[1,3,4],[2,5,6]]
 => 0 = 1 - 1

Description

Eigenvalues of the top-to-random operator acting on a simple module. These eigenvalues are given in [1] and [3]. The simple module of the symmetric group indexed by a partition $\lambda$ has dimension equal to the number of standard tableaux of shape $\lambda$. Hence, the eigenvalues of any linear operator defined on this module can be indexed by standard tableaux of shape $\lambda$; this statistic gives all the eigenvalues of the operator acting on the module. This statistic bears different names, such as the type in [2] or eig in [3]. Similarly, the eigenvalues of the random-to-random operator acting on a simple module is [[St000508]].