Your data matches 4 different statistics following compositions of up to 3 maps.
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Matching statistic: St001564
Mapping
St001564: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 1
[1,1]
 => 3
[3]
 => 1
[2,1]
 => 6
[1,1,1]
 => 10
[4]
 => 1
[3,1]
 => 6
[2,2]
 => 3
[2,1,1]
 => 30
[1,1,1,1]
 => 35
[5]
 => 1
[4,1]
 => 6
[3,2]
 => 6
[3,1,1]
 => 30
[2,2,1]
 => 30
[2,1,1,1]
 => 140
[1,1,1,1,1]
 => 126
[6]
 => 1
[5,1]
 => 6
[4,2]
 => 6
[4,1,1]
 => 30
[3,3]
 => 3
[3,2,1]
 => 60
[3,1,1,1]
 => 140
[2,2,2]
 => 10
[2,2,1,1]
 => 210
[2,1,1,1,1]
 => 630
[1,1,1,1,1,1]
 => 462
[7]
 => 1
[6,1]
 => 6
[5,2]
 => 6
[5,1,1]
 => 30
[4,3]
 => 6
[4,2,1]
 => 60
[4,1,1,1]
 => 140
[3,3,1]
 => 30
[3,2,2]
 => 30
[3,2,1,1]
 => 420
[3,1,1,1,1]
 => 630
[2,2,2,1]
 => 140
[2,2,1,1,1]
 => 1260
[2,1,1,1,1,1]
 => 2772
[1,1,1,1,1,1,1]
 => 1716
Description
The value of the forgotten symmetric functions when all variables set to 1. Let $f_\lambda(x)$ denote the forgotten symmetric functions. Then the statistic associated with $\lambda$, where $\lambda$ has $\ell$ parts, is $f_\lambda(1,1,\dotsc,1)$ where there are $\ell$ variables substituted by $1$.
Matching statistic: St001632
Mapping
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001632: Posets ⟶ ℤResult quality: 6% ●values known / values provided: 14%●distinct values known / distinct values provided: 6%
Values
[1]
 => [[1]]
 => [1] => ([],1)
 => ? = 1
[2]
 => [[1,2]]
 => [1,2] => ([(0,1)],2)
 => 1
[1,1]
 => [[1],[2]]
 => [2,1] => ([],2)
 => ? = 3
[3]
 => [[1,2,3]]
 => [1,2,3] => ([(0,2),(2,1)],3)
 => 1
[2,1]
 => [[1,2],[3]]
 => [3,1,2] => ([(1,2)],3)
 => ? = 6
[1,1,1]
 => [[1],[2],[3]]
 => [3,2,1] => ([],3)
 => ? = 10
[4]
 => [[1,2,3,4]]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 1
[3,1]
 => [[1,2,3],[4]]
 => [4,1,2,3] => ([(1,2),(2,3)],4)
 => ? = 6
[2,2]
 => [[1,2],[3,4]]
 => [3,4,1,2] => ([(0,3),(1,2)],4)
 => ? = 3
[2,1,1]
 => [[1,2],[3],[4]]
 => [4,3,1,2] => ([(2,3)],4)
 => ? = 30
[1,1,1,1]
 => [[1],[2],[3],[4]]
 => [4,3,2,1] => ([],4)
 => ? = 35
[5]
 => [[1,2,3,4,5]]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[4,1]
 => [[1,2,3,4],[5]]
 => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5)
 => ? = 6
[3,2]
 => [[1,2,3],[4,5]]
 => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5)
 => ? = 6
[3,1,1]
 => [[1,2,3],[4],[5]]
 => [5,4,1,2,3] => ([(2,3),(3,4)],5)
 => ? = 30
[2,2,1]
 => [[1,2],[3,4],[5]]
 => [5,3,4,1,2] => ([(1,4),(2,3)],5)
 => ? = 30
[2,1,1,1]
 => [[1,2],[3],[4],[5]]
 => [5,4,3,1,2] => ([(3,4)],5)
 => ? = 140
[1,1,1,1,1]
 => [[1],[2],[3],[4],[5]]
 => [5,4,3,2,1] => ([],5)
 => ? = 126
[6]
 => [[1,2,3,4,5,6]]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,1]
 => [[1,2,3,4,5],[6]]
 => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6)
 => ? = 6
[4,2]
 => [[1,2,3,4],[5,6]]
 => [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6)
 => ? = 6
[4,1,1]
 => [[1,2,3,4],[5],[6]]
 => [6,5,1,2,3,4] => ([(2,3),(3,5),(5,4)],6)
 => ? = 30
[3,3]
 => [[1,2,3],[4,5,6]]
 => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
 => ? = 3
[3,2,1]
 => [[1,2,3],[4,5],[6]]
 => [6,4,5,1,2,3] => ([(1,3),(2,4),(4,5)],6)
 => ? = 60
[3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [6,5,4,1,2,3] => ([(3,4),(4,5)],6)
 => ? = 140
[2,2,2]
 => [[1,2],[3,4],[5,6]]
 => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6)
 => ? = 10
[2,2,1,1]
 => [[1,2],[3,4],[5],[6]]
 => [6,5,3,4,1,2] => ([(2,5),(3,4)],6)
 => ? = 210
[2,1,1,1,1]
 => [[1,2],[3],[4],[5],[6]]
 => [6,5,4,3,1,2] => ([(4,5)],6)
 => ? = 630
[1,1,1,1,1,1]
 => [[1],[2],[3],[4],[5],[6]]
 => [6,5,4,3,2,1] => ([],6)
 => ? = 462
[7]
 => [[1,2,3,4,5,6,7]]
 => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[6,1]
 => [[1,2,3,4,5,6],[7]]
 => [7,1,2,3,4,5,6] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
 => ? = 6
[5,2]
 => [[1,2,3,4,5],[6,7]]
 => [6,7,1,2,3,4,5] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7)
 => ? = 6
[5,1,1]
 => [[1,2,3,4,5],[6],[7]]
 => [7,6,1,2,3,4,5] => ([(2,6),(4,5),(5,3),(6,4)],7)
 => ? = 30
[4,3]
 => [[1,2,3,4],[5,6,7]]
 => [5,6,7,1,2,3,4] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7)
 => ? = 6
[4,2,1]
 => [[1,2,3,4],[5,6],[7]]
 => [7,5,6,1,2,3,4] => ([(1,6),(2,4),(5,3),(6,5)],7)
 => ? = 60
[4,1,1,1]
 => [[1,2,3,4],[5],[6],[7]]
 => [7,6,5,1,2,3,4] => ([(3,4),(4,6),(6,5)],7)
 => ? = 140
[3,3,1]
 => [[1,2,3],[4,5,6],[7]]
 => [7,4,5,6,1,2,3] => ([(1,6),(2,5),(5,3),(6,4)],7)
 => ? = 30
[3,2,2]
 => [[1,2,3],[4,5],[6,7]]
 => [6,7,4,5,1,2,3] => ([(0,5),(1,4),(2,6),(6,3)],7)
 => ? = 30
[3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => ([(2,4),(3,5),(5,6)],7)
 => ? = 420
[3,1,1,1,1]
 => [[1,2,3],[4],[5],[6],[7]]
 => [7,6,5,4,1,2,3] => ([(4,5),(5,6)],7)
 => ? = 630
[2,2,2,1]
 => [[1,2],[3,4],[5,6],[7]]
 => [7,5,6,3,4,1,2] => ([(1,6),(2,5),(3,4)],7)
 => ? = 140
[2,2,1,1,1]
 => [[1,2],[3,4],[5],[6],[7]]
 => [7,6,5,3,4,1,2] => ([(3,6),(4,5)],7)
 => ? = 1260
[2,1,1,1,1,1]
 => [[1,2],[3],[4],[5],[6],[7]]
 => [7,6,5,4,3,1,2] => ([(5,6)],7)
 => ? = 2772
[1,1,1,1,1,1,1]
 => [[1],[2],[3],[4],[5],[6],[7]]
 => [7,6,5,4,3,2,1] => ([],7)
 => ? = 1716
Description
The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset.
Matching statistic: St001695
Mapping
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
St001695: Standard tableaux ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 19%
Values
[1]
 => [1,0,1,0]
 => [1,1,0,1,0,0]
 => [[1,2,4],[3,5,6]]
 => 3 = 1 + 2
[2]
 => [1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [[1,2,3,6],[4,5,7,8]]
 => 3 = 1 + 2
[1,1]
 => [1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [[1,2,4,5],[3,6,7,8]]
 => 5 = 3 + 2
[3]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [[1,2,3,4,8],[5,6,7,9,10]]
 => ? = 1 + 2
[2,1]
 => [1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [[1,2,4,6],[3,5,7,8]]
 => 8 = 6 + 2
[1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [[1,2,4,5,6],[3,7,8,9,10]]
 => ? = 10 + 2
[4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [[1,2,3,4,5,10],[6,7,8,9,11,12]]
 => ? = 1 + 2
[3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [[1,2,3,5,8],[4,6,7,9,10]]
 => ? = 6 + 2
[2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [[1,2,3,6,7],[4,5,8,9,10]]
 => ? = 3 + 2
[2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [[1,2,4,5,7],[3,6,8,9,10]]
 => ? = 30 + 2
[1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [[1,2,4,5,6,7],[3,8,9,10,11,12]]
 => ? = 35 + 2
[5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => [[1,2,3,4,5,6,12],[7,8,9,10,11,13,14]]
 => ? = 1 + 2
[4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0]
 => [[1,2,3,4,6,10],[5,7,8,9,11,12]]
 => ? = 6 + 2
[3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[1,2,3,6,8],[4,5,7,9,10]]
 => ? = 6 + 2
[3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [[1,2,4,5,8],[3,6,7,9,10]]
 => ? = 30 + 2
[2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [[1,2,4,6,7],[3,5,8,9,10]]
 => ? = 30 + 2
[2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => [[1,2,4,5,6,8],[3,7,9,10,11,12]]
 => ? = 140 + 2
[1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => [[1,2,4,5,6,7,8],[3,9,10,11,12,13,14]]
 => ? = 126 + 2
[6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
 => [[1,2,3,4,5,6,7,14],[8,9,10,11,12,13,15,16]]
 => ? = 1 + 2
[5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,1,1,1,1,0,1,0,0,0,0,1,0,0]
 => [[1,2,3,4,5,7,12],[6,8,9,10,11,13,14]]
 => ? = 6 + 2
[4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => [[1,2,3,4,7,10],[5,6,8,9,11,12]]
 => ? = 6 + 2
[4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => [[1,2,3,5,6,10],[4,7,8,9,11,12]]
 => ? = 30 + 2
[3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [[1,2,3,4,8,9],[5,6,7,10,11,12]]
 => ? = 3 + 2
[3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [[1,2,4,6,8],[3,5,7,9,10]]
 => ? = 60 + 2
[3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => [[1,2,4,5,6,9],[3,7,8,10,11,12]]
 => ? = 140 + 2
[2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [[1,2,3,6,7,8],[4,5,9,10,11,12]]
 => ? = 10 + 2
[2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [[1,2,4,5,7,8],[3,6,9,10,11,12]]
 => ? = 210 + 2
[2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
 => [[1,2,4,5,6,7,9],[3,8,10,11,12,13,14]]
 => ? = 630 + 2
[1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [[1,2,4,5,6,7,8,9],[3,10,11,12,13,14,15,16]]
 => ? = 462 + 2
[7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
 => [[1,2,3,4,5,6,7,8,16],[9,10,11,12,13,14,15,17,18]]
 => ? = 1 + 2
[6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
 => [[1,2,3,4,5,6,8,14],[7,9,10,11,12,13,15,16]]
 => ? = 6 + 2
[5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,1,0,0]
 => [[1,2,3,4,5,8,12],[6,7,9,10,11,13,14]]
 => ? = 6 + 2
[5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,1,0,0]
 => [[1,2,3,4,6,7,12],[5,8,9,10,11,13,14]]
 => ? = 30 + 2
[4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [[1,2,3,4,8,10],[5,6,7,9,11,12]]
 => ? = 6 + 2
[4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [[1,2,3,5,7,10],[4,6,8,9,11,12]]
 => ? = 60 + 2
[4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [[1,2,4,5,6,10],[3,7,8,9,11,12]]
 => ? = 140 + 2
[3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,1,0,0,0]
 => [[1,2,3,5,8,9],[4,6,7,10,11,12]]
 => ? = 30 + 2
[3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,1,0,1,0,0,0]
 => [[1,2,3,6,7,9],[4,5,8,10,11,12]]
 => ? = 30 + 2
[3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => [[1,2,4,5,7,9],[3,6,8,10,11,12]]
 => ? = 420 + 2
[3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,1,1,0,0,1,0,0,0,0]
 => [[1,2,4,5,6,7,10],[3,8,9,11,12,13,14]]
 => ? = 630 + 2
[2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [[1,2,4,6,7,8],[3,5,9,10,11,12]]
 => ? = 140 + 2
[2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,1,0,1,1,1,0,1,1,0,0,0,0,0]
 => [[1,2,4,5,6,8,9],[3,7,10,11,12,13,14]]
 => ? = 1260 + 2
[2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [[1,2,4,5,6,7,8,10],[3,9,11,12,13,14,15,16]]
 => ? = 2772 + 2
[1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
 => [[1,2,4,5,6,7,8,9,10],[3,11,12,13,14,15,16,17,18]]
 => ? = 1716 + 2
Description
The natural comajor index of a standard Young tableau. A natural descent of a standard tableau $T$ is an entry $i$ such that $i+1$ appears in a higher row than $i$ in English notation. The natural comajor index of a tableau of size $n$ with natural descent set $D$ is then $\sum_{d\in D} n-d$.
Matching statistic: St001698
Mapping
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
St001698: Standard tableaux ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 19%
Values
[1]
 => [1,0,1,0]
 => [1,1,0,1,0,0]
 => [[1,2,4],[3,5,6]]
 => 3 = 1 + 2
[2]
 => [1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [[1,2,3,6],[4,5,7,8]]
 => 3 = 1 + 2
[1,1]
 => [1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [[1,2,4,5],[3,6,7,8]]
 => 5 = 3 + 2
[3]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [[1,2,3,4,8],[5,6,7,9,10]]
 => ? = 1 + 2
[2,1]
 => [1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [[1,2,4,6],[3,5,7,8]]
 => 8 = 6 + 2
[1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [[1,2,4,5,6],[3,7,8,9,10]]
 => ? = 10 + 2
[4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [[1,2,3,4,5,10],[6,7,8,9,11,12]]
 => ? = 1 + 2
[3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [[1,2,3,5,8],[4,6,7,9,10]]
 => ? = 6 + 2
[2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [[1,2,3,6,7],[4,5,8,9,10]]
 => ? = 3 + 2
[2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [[1,2,4,5,7],[3,6,8,9,10]]
 => ? = 30 + 2
[1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [[1,2,4,5,6,7],[3,8,9,10,11,12]]
 => ? = 35 + 2
[5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => [[1,2,3,4,5,6,12],[7,8,9,10,11,13,14]]
 => ? = 1 + 2
[4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0]
 => [[1,2,3,4,6,10],[5,7,8,9,11,12]]
 => ? = 6 + 2
[3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[1,2,3,6,8],[4,5,7,9,10]]
 => ? = 6 + 2
[3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [[1,2,4,5,8],[3,6,7,9,10]]
 => ? = 30 + 2
[2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [[1,2,4,6,7],[3,5,8,9,10]]
 => ? = 30 + 2
[2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => [[1,2,4,5,6,8],[3,7,9,10,11,12]]
 => ? = 140 + 2
[1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => [[1,2,4,5,6,7,8],[3,9,10,11,12,13,14]]
 => ? = 126 + 2
[6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
 => [[1,2,3,4,5,6,7,14],[8,9,10,11,12,13,15,16]]
 => ? = 1 + 2
[5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,1,1,1,1,0,1,0,0,0,0,1,0,0]
 => [[1,2,3,4,5,7,12],[6,8,9,10,11,13,14]]
 => ? = 6 + 2
[4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => [[1,2,3,4,7,10],[5,6,8,9,11,12]]
 => ? = 6 + 2
[4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => [[1,2,3,5,6,10],[4,7,8,9,11,12]]
 => ? = 30 + 2
[3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [[1,2,3,4,8,9],[5,6,7,10,11,12]]
 => ? = 3 + 2
[3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [[1,2,4,6,8],[3,5,7,9,10]]
 => ? = 60 + 2
[3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => [[1,2,4,5,6,9],[3,7,8,10,11,12]]
 => ? = 140 + 2
[2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [[1,2,3,6,7,8],[4,5,9,10,11,12]]
 => ? = 10 + 2
[2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [[1,2,4,5,7,8],[3,6,9,10,11,12]]
 => ? = 210 + 2
[2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
 => [[1,2,4,5,6,7,9],[3,8,10,11,12,13,14]]
 => ? = 630 + 2
[1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [[1,2,4,5,6,7,8,9],[3,10,11,12,13,14,15,16]]
 => ? = 462 + 2
[7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
 => [[1,2,3,4,5,6,7,8,16],[9,10,11,12,13,14,15,17,18]]
 => ? = 1 + 2
[6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
 => [[1,2,3,4,5,6,8,14],[7,9,10,11,12,13,15,16]]
 => ? = 6 + 2
[5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,1,0,0]
 => [[1,2,3,4,5,8,12],[6,7,9,10,11,13,14]]
 => ? = 6 + 2
[5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,1,0,0]
 => [[1,2,3,4,6,7,12],[5,8,9,10,11,13,14]]
 => ? = 30 + 2
[4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [[1,2,3,4,8,10],[5,6,7,9,11,12]]
 => ? = 6 + 2
[4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [[1,2,3,5,7,10],[4,6,8,9,11,12]]
 => ? = 60 + 2
[4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [[1,2,4,5,6,10],[3,7,8,9,11,12]]
 => ? = 140 + 2
[3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,1,0,0,0]
 => [[1,2,3,5,8,9],[4,6,7,10,11,12]]
 => ? = 30 + 2
[3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,1,0,1,0,0,0]
 => [[1,2,3,6,7,9],[4,5,8,10,11,12]]
 => ? = 30 + 2
[3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => [[1,2,4,5,7,9],[3,6,8,10,11,12]]
 => ? = 420 + 2
[3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,1,1,0,0,1,0,0,0,0]
 => [[1,2,4,5,6,7,10],[3,8,9,11,12,13,14]]
 => ? = 630 + 2
[2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [[1,2,4,6,7,8],[3,5,9,10,11,12]]
 => ? = 140 + 2
[2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,1,0,1,1,1,0,1,1,0,0,0,0,0]
 => [[1,2,4,5,6,8,9],[3,7,10,11,12,13,14]]
 => ? = 1260 + 2
[2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [[1,2,4,5,6,7,8,10],[3,9,11,12,13,14,15,16]]
 => ? = 2772 + 2
[1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
 => [[1,2,4,5,6,7,8,9,10],[3,11,12,13,14,15,16,17,18]]
 => ? = 1716 + 2
Description
The comajor index of a standard tableau minus the weighted size of its shape.