Your data matches 4 different statistics following compositions of up to 3 maps.
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Matching statistic: St000003
(load all 2 compositions to match this statistic)
Mapping
Mp00040: Integer compositions —to partition⟶ Integer partitions
St000003: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [1]
 => 1
[1,1] => [1,1]
 => 1
[2] => [2]
 => 1
[1,1,1] => [1,1,1]
 => 1
[1,2] => [2,1]
 => 2
[2,1] => [2,1]
 => 2
[3] => [3]
 => 1
[1,1,1,1] => [1,1,1,1]
 => 1
[1,1,2] => [2,1,1]
 => 3
[1,2,1] => [2,1,1]
 => 3
[1,3] => [3,1]
 => 3
[2,1,1] => [2,1,1]
 => 3
[2,2] => [2,2]
 => 2
[3,1] => [3,1]
 => 3
[4] => [4]
 => 1
[1,1,1,1,1] => [1,1,1,1,1]
 => 1
[1,1,1,2] => [2,1,1,1]
 => 4
[1,1,2,1] => [2,1,1,1]
 => 4
[1,1,3] => [3,1,1]
 => 6
[1,2,1,1] => [2,1,1,1]
 => 4
[1,2,2] => [2,2,1]
 => 5
[1,3,1] => [3,1,1]
 => 6
[1,4] => [4,1]
 => 4
[2,1,1,1] => [2,1,1,1]
 => 4
[2,1,2] => [2,2,1]
 => 5
[2,2,1] => [2,2,1]
 => 5
[2,3] => [3,2]
 => 5
[3,1,1] => [3,1,1]
 => 6
[3,2] => [3,2]
 => 5
[4,1] => [4,1]
 => 4
[5] => [5]
 => 1
[1,1,1,1,1,1] => [1,1,1,1,1,1]
 => 1
[1,1,1,1,2] => [2,1,1,1,1]
 => 5
[1,1,1,2,1] => [2,1,1,1,1]
 => 5
[1,1,1,3] => [3,1,1,1]
 => 10
[1,1,2,1,1] => [2,1,1,1,1]
 => 5
[1,1,2,2] => [2,2,1,1]
 => 9
[1,1,3,1] => [3,1,1,1]
 => 10
[1,1,4] => [4,1,1]
 => 10
[1,2,1,1,1] => [2,1,1,1,1]
 => 5
[1,2,1,2] => [2,2,1,1]
 => 9
[1,2,2,1] => [2,2,1,1]
 => 9
[1,2,3] => [3,2,1]
 => 16
[1,3,1,1] => [3,1,1,1]
 => 10
[1,3,2] => [3,2,1]
 => 16
[1,4,1] => [4,1,1]
 => 10
[1,5] => [5,1]
 => 5
[2,1,1,1,1] => [2,1,1,1,1]
 => 5
[2,1,1,2] => [2,2,1,1]
 => 9
[2,1,2,1] => [2,2,1,1]
 => 9
Description
The number of [[/StandardTableaux|standard Young tableaux]] of the partition.
Matching statistic: St000100
Mapping
Mp00040: Integer compositions —to partition⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St000100: Posets ⟶ ℤResult quality: 46% ●values known / values provided: 54%●distinct values known / distinct values provided: 46%
Values
[1] => [1]
 => [[1],[]]
 => ([],1)
 => ? = 1
[1,1] => [1,1]
 => [[1,1],[]]
 => ([(0,1)],2)
 => 1
[2] => [2]
 => [[2],[]]
 => ([(0,1)],2)
 => 1
[1,1,1] => [1,1,1]
 => [[1,1,1],[]]
 => ([(0,2),(2,1)],3)
 => 1
[1,2] => [2,1]
 => [[2,1],[]]
 => ([(0,1),(0,2)],3)
 => 2
[2,1] => [2,1]
 => [[2,1],[]]
 => ([(0,1),(0,2)],3)
 => 2
[3] => [3]
 => [[3],[]]
 => ([(0,2),(2,1)],3)
 => 1
[1,1,1,1] => [1,1,1,1]
 => [[1,1,1,1],[]]
 => ([(0,3),(2,1),(3,2)],4)
 => 1
[1,1,2] => [2,1,1]
 => [[2,1,1],[]]
 => ([(0,2),(0,3),(3,1)],4)
 => 3
[1,2,1] => [2,1,1]
 => [[2,1,1],[]]
 => ([(0,2),(0,3),(3,1)],4)
 => 3
[1,3] => [3,1]
 => [[3,1],[]]
 => ([(0,2),(0,3),(3,1)],4)
 => 3
[2,1,1] => [2,1,1]
 => [[2,1,1],[]]
 => ([(0,2),(0,3),(3,1)],4)
 => 3
[2,2] => [2,2]
 => [[2,2],[]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[3,1] => [3,1]
 => [[3,1],[]]
 => ([(0,2),(0,3),(3,1)],4)
 => 3
[4] => [4]
 => [[4],[]]
 => ([(0,3),(2,1),(3,2)],4)
 => 1
[1,1,1,1,1] => [1,1,1,1,1]
 => [[1,1,1,1,1],[]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[1,1,1,2] => [2,1,1,1]
 => [[2,1,1,1],[]]
 => ([(0,2),(0,4),(3,1),(4,3)],5)
 => 4
[1,1,2,1] => [2,1,1,1]
 => [[2,1,1,1],[]]
 => ([(0,2),(0,4),(3,1),(4,3)],5)
 => 4
[1,1,3] => [3,1,1]
 => [[3,1,1],[]]
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => 6
[1,2,1,1] => [2,1,1,1]
 => [[2,1,1,1],[]]
 => ([(0,2),(0,4),(3,1),(4,3)],5)
 => 4
[1,2,2] => [2,2,1]
 => [[2,2,1],[]]
 => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 5
[1,3,1] => [3,1,1]
 => [[3,1,1],[]]
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => 6
[1,4] => [4,1]
 => [[4,1],[]]
 => ([(0,2),(0,4),(3,1),(4,3)],5)
 => 4
[2,1,1,1] => [2,1,1,1]
 => [[2,1,1,1],[]]
 => ([(0,2),(0,4),(3,1),(4,3)],5)
 => 4
[2,1,2] => [2,2,1]
 => [[2,2,1],[]]
 => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 5
[2,2,1] => [2,2,1]
 => [[2,2,1],[]]
 => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 5
[2,3] => [3,2]
 => [[3,2],[]]
 => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 5
[3,1,1] => [3,1,1]
 => [[3,1,1],[]]
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => 6
[3,2] => [3,2]
 => [[3,2],[]]
 => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 5
[4,1] => [4,1]
 => [[4,1],[]]
 => ([(0,2),(0,4),(3,1),(4,3)],5)
 => 4
[5] => [5]
 => [[5],[]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[1,1,1,1,1,1] => [1,1,1,1,1,1]
 => [[1,1,1,1,1,1],[]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[1,1,1,1,2] => [2,1,1,1,1]
 => [[2,1,1,1,1],[]]
 => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => 5
[1,1,1,2,1] => [2,1,1,1,1]
 => [[2,1,1,1,1],[]]
 => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => 5
[1,1,1,3] => [3,1,1,1]
 => [[3,1,1,1],[]]
 => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => 10
[1,1,2,1,1] => [2,1,1,1,1]
 => [[2,1,1,1,1],[]]
 => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => 5
[1,1,2,2] => [2,2,1,1]
 => [[2,2,1,1],[]]
 => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
 => 9
[1,1,3,1] => [3,1,1,1]
 => [[3,1,1,1],[]]
 => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => 10
[1,1,4] => [4,1,1]
 => [[4,1,1],[]]
 => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => 10
[1,2,1,1,1] => [2,1,1,1,1]
 => [[2,1,1,1,1],[]]
 => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => 5
[1,2,1,2] => [2,2,1,1]
 => [[2,2,1,1],[]]
 => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
 => 9
[1,2,2,1] => [2,2,1,1]
 => [[2,2,1,1],[]]
 => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
 => 9
[1,2,3] => [3,2,1]
 => [[3,2,1],[]]
 => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
 => 16
[1,3,1,1] => [3,1,1,1]
 => [[3,1,1,1],[]]
 => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => 10
[1,3,2] => [3,2,1]
 => [[3,2,1],[]]
 => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
 => 16
[1,4,1] => [4,1,1]
 => [[4,1,1],[]]
 => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => 10
[1,5] => [5,1]
 => [[5,1],[]]
 => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => 5
[2,1,1,1,1] => [2,1,1,1,1]
 => [[2,1,1,1,1],[]]
 => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => 5
[2,1,1,2] => [2,2,1,1]
 => [[2,2,1,1],[]]
 => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
 => 9
[2,1,2,1] => [2,2,1,1]
 => [[2,2,1,1],[]]
 => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
 => 9
[2,1,3] => [3,2,1]
 => [[3,2,1],[]]
 => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
 => 16
[1,10] => [10,1]
 => [[10,1],[]]
 => ?
 => ? = 10
[1,8,1,1] => [8,1,1,1]
 => [[8,1,1,1],[]]
 => ?
 => ? = 120
[1,7,2,1] => [7,2,1,1]
 => [[7,2,1,1],[]]
 => ?
 => ? = 594
[1,6,3,1] => [6,3,1,1]
 => [[6,3,1,1],[]]
 => ?
 => ? = 1232
[1,5,4,1] => [5,4,1,1]
 => [[5,4,1,1],[]]
 => ([(0,6),(0,7),(3,2),(4,5),(4,10),(5,1),(5,9),(6,4),(6,8),(7,3),(7,8),(8,10),(10,9)],11)
 => ? = 1155
[1,4,5,1] => [5,4,1,1]
 => [[5,4,1,1],[]]
 => ([(0,6),(0,7),(3,2),(4,5),(4,10),(5,1),(5,9),(6,4),(6,8),(7,3),(7,8),(8,10),(10,9)],11)
 => ? = 1155
[1,3,6,1] => [6,3,1,1]
 => [[6,3,1,1],[]]
 => ?
 => ? = 1232
[1,2,7,1] => [7,2,1,1]
 => [[7,2,1,1],[]]
 => ?
 => ? = 594
[1,1,8,1] => [8,1,1,1]
 => [[8,1,1,1],[]]
 => ?
 => ? = 120
[10,1] => [10,1]
 => [[10,1],[]]
 => ?
 => ? = 10
[1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1]
 => [[1,1,1,1,1,1,1,1,1,1,1,1],[]]
 => ?
 => ? = 1
[1,1,1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1,1,1]
 => [[2,2,1,1,1,1,1,1,1,1],[]]
 => ?
 => ? = 54
[1,1,1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1,1,1]
 => [[2,2,1,1,1,1,1,1,1,1],[]]
 => ?
 => ? = 54
[1,1,1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1,1,1]
 => [[2,2,1,1,1,1,1,1,1,1],[]]
 => ?
 => ? = 54
[1,1,1,1,1,1,3,3] => [3,3,1,1,1,1,1,1]
 => [[3,3,1,1,1,1,1,1],[]]
 => ?
 => ? = 616
[1,1,1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
 => [[2,2,1,1,1,1,1,1,1,1],[]]
 => ?
 => ? = 54
[1,1,1,1,2,2,2,2] => [2,2,2,2,1,1,1,1]
 => [[2,2,2,2,1,1,1,1],[]]
 => ?
 => ? = 275
[1,1,1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1]
 => [[2,2,1,1,1,1,1,1,1,1],[]]
 => ?
 => ? = 54
[1,1,1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1]
 => [[2,2,1,1,1,1,1,1,1,1],[]]
 => ?
 => ? = 54
[1,1,1,1,2,1,2,3] => [3,2,2,1,1,1,1,1]
 => [[3,2,2,1,1,1,1,1],[]]
 => ?
 => ? = 891
[1,1,1,1,3,3,1,1] => [3,3,1,1,1,1,1,1]
 => [[3,3,1,1,1,1,1,1],[]]
 => ?
 => ? = 616
[1,1,1,1,3,2,1,2] => [3,2,2,1,1,1,1,1]
 => [[3,2,2,1,1,1,1,1],[]]
 => ?
 => ? = 891
[1,1,1,1,3,1,1,3] => [3,3,1,1,1,1,1,1]
 => [[3,3,1,1,1,1,1,1],[]]
 => ?
 => ? = 616
[1,1,1,1,4,4] => [4,4,1,1,1,1]
 => [[4,4,1,1,1,1],[]]
 => ?
 => ? = 1925
[1,1,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
 => [[2,2,1,1,1,1,1,1,1,1],[]]
 => ?
 => ? = 54
[1,1,2,2,1,1,2,2] => [2,2,2,2,1,1,1,1]
 => [[2,2,2,2,1,1,1,1],[]]
 => ?
 => ? = 275
[1,1,2,2,2,2,1,1] => [2,2,2,2,1,1,1,1]
 => [[2,2,2,2,1,1,1,1],[]]
 => ?
 => ? = 275
[1,1,2,2,2,1,1,2] => [2,2,2,2,1,1,1,1]
 => [[2,2,2,2,1,1,1,1],[]]
 => ?
 => ? = 275
[1,1,2,2,3,3] => [3,3,2,2,1,1]
 => [[3,3,2,2,1,1],[]]
 => ([(0,6),(0,7),(2,10),(3,1),(4,3),(4,9),(5,4),(5,11),(6,5),(6,8),(7,2),(7,8),(8,10),(8,11),(11,9)],12)
 => ? = 2673
[1,1,2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
 => [[2,2,1,1,1,1,1,1,1,1],[]]
 => ?
 => ? = 54
[1,1,2,1,1,2,2,2] => [2,2,2,2,1,1,1,1]
 => [[2,2,2,2,1,1,1,1],[]]
 => ?
 => ? = 275
[1,1,2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1]
 => [[2,2,1,1,1,1,1,1,1,1],[]]
 => ?
 => ? = 54
[1,1,2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1]
 => [[2,2,1,1,1,1,1,1,1,1],[]]
 => ?
 => ? = 54
[1,1,2,1,1,1,2,3] => [3,2,2,1,1,1,1,1]
 => [[3,2,2,1,1,1,1,1],[]]
 => ?
 => ? = 891
[1,1,2,1,2,3,1,1] => [3,2,2,1,1,1,1,1]
 => [[3,2,2,1,1,1,1,1],[]]
 => ?
 => ? = 891
[1,1,2,1,2,2,1,2] => [2,2,2,2,1,1,1,1]
 => [[2,2,2,2,1,1,1,1],[]]
 => ?
 => ? = 275
[1,1,2,1,2,1,1,3] => [3,2,2,1,1,1,1,1]
 => [[3,2,2,1,1,1,1,1],[]]
 => ?
 => ? = 891
[1,1,2,1,3,4] => [4,3,2,1,1,1]
 => [[4,3,2,1,1,1],[]]
 => ?
 => ? = 5632
[1,1,3,3,1,1,1,1] => [3,3,1,1,1,1,1,1]
 => [[3,3,1,1,1,1,1,1],[]]
 => ?
 => ? = 616
[1,1,3,3,2,2] => [3,3,2,2,1,1]
 => [[3,3,2,2,1,1],[]]
 => ([(0,6),(0,7),(2,10),(3,1),(4,3),(4,9),(5,4),(5,11),(6,5),(6,8),(7,2),(7,8),(8,10),(8,11),(11,9)],12)
 => ? = 2673
[1,1,3,2,1,2,1,1] => [3,2,2,1,1,1,1,1]
 => [[3,2,2,1,1,1,1,1],[]]
 => ?
 => ? = 891
[1,1,3,2,1,1,1,2] => [3,2,2,1,1,1,1,1]
 => [[3,2,2,1,1,1,1,1],[]]
 => ?
 => ? = 891
[1,1,3,2,2,3] => [3,3,2,2,1,1]
 => [[3,3,2,2,1,1],[]]
 => ([(0,6),(0,7),(2,10),(3,1),(4,3),(4,9),(5,4),(5,11),(6,5),(6,8),(7,2),(7,8),(8,10),(8,11),(11,9)],12)
 => ? = 2673
[1,1,3,1,1,3,1,1] => [3,3,1,1,1,1,1,1]
 => [[3,3,1,1,1,1,1,1],[]]
 => ?
 => ? = 616
[1,1,3,1,1,2,1,2] => [3,2,2,1,1,1,1,1]
 => [[3,2,2,1,1,1,1,1],[]]
 => ?
 => ? = 891
[1,1,3,1,1,1,1,3] => [3,3,1,1,1,1,1,1]
 => [[3,3,1,1,1,1,1,1],[]]
 => ?
 => ? = 616
[1,1,3,1,2,4] => [4,3,2,1,1,1]
 => [[4,3,2,1,1,1],[]]
 => ?
 => ? = 5632
[1,1,4,4,1,1] => [4,4,1,1,1,1]
 => [[4,4,1,1,1,1],[]]
 => ?
 => ? = 1925
[1,1,4,3,1,2] => [4,3,2,1,1,1]
 => [[4,3,2,1,1,1],[]]
 => ?
 => ? = 5632
Description
The number of linear extensions of a poset.
Matching statistic: St000001
Mapping
Mp00040: Integer compositions —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
St000001: Permutations ⟶ ℤResult quality: 51% ●values known / values provided: 51%●distinct values known / distinct values provided: 55%
Values
[1] => [1]
 => [1,0,1,0]
 => [2,1] => 1
[1,1] => [1,1]
 => [1,0,1,1,0,0]
 => [2,3,1] => 1
[2] => [2]
 => [1,1,0,0,1,0]
 => [3,1,2] => 1
[1,1,1] => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [2,3,4,1] => 1
[1,2] => [2,1]
 => [1,0,1,0,1,0]
 => [3,2,1] => 2
[2,1] => [2,1]
 => [1,0,1,0,1,0]
 => [3,2,1] => 2
[3] => [3]
 => [1,1,1,0,0,0,1,0]
 => [4,1,2,3] => 1
[1,1,1,1] => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => 1
[1,1,2] => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [3,2,4,1] => 3
[1,2,1] => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [3,2,4,1] => 3
[1,3] => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [4,2,1,3] => 3
[2,1,1] => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [3,2,4,1] => 3
[2,2] => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [3,4,1,2] => 2
[3,1] => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [4,2,1,3] => 3
[4] => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => 1
[1,1,1,1,1] => [1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [2,3,4,5,6,1] => 1
[1,1,1,2] => [2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [3,2,4,5,1] => 4
[1,1,2,1] => [2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [3,2,4,5,1] => 4
[1,1,3] => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [4,2,3,1] => 6
[1,2,1,1] => [2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [3,2,4,5,1] => 4
[1,2,2] => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [3,4,2,1] => 5
[1,3,1] => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [4,2,3,1] => 6
[1,4] => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [5,2,1,3,4] => 4
[2,1,1,1] => [2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [3,2,4,5,1] => 4
[2,1,2] => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [3,4,2,1] => 5
[2,2,1] => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [3,4,2,1] => 5
[2,3] => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [4,3,1,2] => 5
[3,1,1] => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [4,2,3,1] => 6
[3,2] => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [4,3,1,2] => 5
[4,1] => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [5,2,1,3,4] => 4
[5] => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [6,1,2,3,4,5] => 1
[1,1,1,1,1,1] => [1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [2,3,4,5,6,7,1] => 1
[1,1,1,1,2] => [2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [3,2,4,5,6,1] => 5
[1,1,1,2,1] => [2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [3,2,4,5,6,1] => 5
[1,1,1,3] => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [4,2,3,5,1] => 10
[1,1,2,1,1] => [2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [3,2,4,5,6,1] => 5
[1,1,2,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [3,4,2,5,1] => 9
[1,1,3,1] => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [4,2,3,5,1] => 10
[1,1,4] => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [5,2,3,1,4] => 10
[1,2,1,1,1] => [2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [3,2,4,5,6,1] => 5
[1,2,1,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [3,4,2,5,1] => 9
[1,2,2,1] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [3,4,2,5,1] => 9
[1,2,3] => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [4,3,2,1] => 16
[1,3,1,1] => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [4,2,3,5,1] => 10
[1,3,2] => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [4,3,2,1] => 16
[1,4,1] => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [5,2,3,1,4] => 10
[1,5] => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [6,2,1,3,4,5] => 5
[2,1,1,1,1] => [2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [3,2,4,5,6,1] => 5
[2,1,1,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [3,4,2,5,1] => 9
[2,1,2,1] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [3,4,2,5,1] => 9
[1,1,1,1,1,1,1] => [1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [2,3,4,5,6,7,8,1] => ? = 1
[7] => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [8,1,2,3,4,5,6,7] => ? = 1
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
 => [2,3,4,5,6,7,8,9,1] => ? = 1
[1,1,1,1,1,1,2] => [2,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [3,2,4,5,6,7,8,1] => ? = 7
[1,1,1,1,1,2,1] => [2,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [3,2,4,5,6,7,8,1] => ? = 7
[1,1,1,1,2,1,1] => [2,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [3,2,4,5,6,7,8,1] => ? = 7
[1,1,1,2,1,1,1] => [2,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [3,2,4,5,6,7,8,1] => ? = 7
[1,1,2,1,1,1,1] => [2,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [3,2,4,5,6,7,8,1] => ? = 7
[1,2,1,1,1,1,1] => [2,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [3,2,4,5,6,7,8,1] => ? = 7
[1,7] => [7,1]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
 => [8,2,1,3,4,5,6,7] => ? = 7
[2,1,1,1,1,1,1] => [2,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [3,2,4,5,6,7,8,1] => ? = 7
[7,1] => [7,1]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
 => [8,2,1,3,4,5,6,7] => ? = 7
[8] => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [9,1,2,3,4,5,6,7,8] => ? = 1
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
 => [2,3,4,5,6,7,8,9,10,1] => ? = 1
[1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [3,2,4,5,6,7,8,9,1] => ? = 8
[1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [3,2,4,5,6,7,8,9,1] => ? = 8
[1,1,1,1,1,1,3] => [3,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => [4,2,3,5,6,7,8,1] => ? = 28
[1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [3,2,4,5,6,7,8,9,1] => ? = 8
[1,1,1,1,1,2,2] => [2,2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [3,4,2,5,6,7,8,1] => ? = 27
[1,1,1,1,1,3,1] => [3,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => [4,2,3,5,6,7,8,1] => ? = 28
[1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [3,2,4,5,6,7,8,9,1] => ? = 8
[1,1,1,1,2,1,2] => [2,2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [3,4,2,5,6,7,8,1] => ? = 27
[1,1,1,1,2,2,1] => [2,2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [3,4,2,5,6,7,8,1] => ? = 27
[1,1,1,1,3,1,1] => [3,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => [4,2,3,5,6,7,8,1] => ? = 28
[1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [3,2,4,5,6,7,8,9,1] => ? = 8
[1,1,1,2,1,1,2] => [2,2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [3,4,2,5,6,7,8,1] => ? = 27
[1,1,1,2,1,2,1] => [2,2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [3,4,2,5,6,7,8,1] => ? = 27
[1,1,1,2,2,1,1] => [2,2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [3,4,2,5,6,7,8,1] => ? = 27
[1,1,1,3,1,1,1] => [3,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => [4,2,3,5,6,7,8,1] => ? = 28
[1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [3,2,4,5,6,7,8,9,1] => ? = 8
[1,1,2,1,1,1,2] => [2,2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [3,4,2,5,6,7,8,1] => ? = 27
[1,1,2,1,1,2,1] => [2,2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [3,4,2,5,6,7,8,1] => ? = 27
[1,1,2,1,2,1,1] => [2,2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [3,4,2,5,6,7,8,1] => ? = 27
[1,1,2,2,1,1,1] => [2,2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [3,4,2,5,6,7,8,1] => ? = 27
[1,1,3,1,1,1,1] => [3,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => [4,2,3,5,6,7,8,1] => ? = 28
[1,1,7] => [7,1,1]
 => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
 => [8,2,3,1,4,5,6,7] => ? = 28
[1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [3,2,4,5,6,7,8,9,1] => ? = 8
[1,2,1,1,1,1,2] => [2,2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [3,4,2,5,6,7,8,1] => ? = 27
[1,2,1,1,1,2,1] => [2,2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [3,4,2,5,6,7,8,1] => ? = 27
[1,2,1,1,2,1,1] => [2,2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [3,4,2,5,6,7,8,1] => ? = 27
[1,2,1,2,1,1,1] => [2,2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [3,4,2,5,6,7,8,1] => ? = 27
[1,2,2,1,1,1,1] => [2,2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [3,4,2,5,6,7,8,1] => ? = 27
[1,3,1,1,1,1,1] => [3,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => [4,2,3,5,6,7,8,1] => ? = 28
[1,7,1] => [7,1,1]
 => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
 => [8,2,3,1,4,5,6,7] => ? = 28
[1,8] => [8,1]
 => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
 => [9,2,1,3,4,5,6,7,8] => ? = 8
[2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [3,2,4,5,6,7,8,9,1] => ? = 8
[2,1,1,1,1,1,2] => [2,2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [3,4,2,5,6,7,8,1] => ? = 27
[2,1,1,1,1,2,1] => [2,2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [3,4,2,5,6,7,8,1] => ? = 27
[2,1,1,1,2,1,1] => [2,2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [3,4,2,5,6,7,8,1] => ? = 27
[2,1,1,2,1,1,1] => [2,2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [3,4,2,5,6,7,8,1] => ? = 27
Description
The number of reduced words for a permutation. This is the number of ways to write a permutation as a minimal length product of simple transpositions. E.g., there are two reduced words for the permutation $[3,2,1]$, which are $(1,2)(2,3)(1,2) = (2,3)(1,2)(2,3)$.
Matching statistic: St001595
(load all 3 compositions to match this statistic)
Mapping
Mp00040: Integer compositions —to partition⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
St001595: Skew partitions ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 14%
Values
[1] => [1]
 => [[1],[]]
 => 1
[1,1] => [1,1]
 => [[1,1],[]]
 => 1
[2] => [2]
 => [[2],[]]
 => 1
[1,1,1] => [1,1,1]
 => [[1,1,1],[]]
 => 1
[1,2] => [2,1]
 => [[2,1],[]]
 => 2
[2,1] => [2,1]
 => [[2,1],[]]
 => 2
[3] => [3]
 => [[3],[]]
 => 1
[1,1,1,1] => [1,1,1,1]
 => [[1,1,1,1],[]]
 => 1
[1,1,2] => [2,1,1]
 => [[2,1,1],[]]
 => 3
[1,2,1] => [2,1,1]
 => [[2,1,1],[]]
 => 3
[1,3] => [3,1]
 => [[3,1],[]]
 => 3
[2,1,1] => [2,1,1]
 => [[2,1,1],[]]
 => 3
[2,2] => [2,2]
 => [[2,2],[]]
 => 2
[3,1] => [3,1]
 => [[3,1],[]]
 => 3
[4] => [4]
 => [[4],[]]
 => 1
[1,1,1,1,1] => [1,1,1,1,1]
 => [[1,1,1,1,1],[]]
 => 1
[1,1,1,2] => [2,1,1,1]
 => [[2,1,1,1],[]]
 => 4
[1,1,2,1] => [2,1,1,1]
 => [[2,1,1,1],[]]
 => 4
[1,1,3] => [3,1,1]
 => [[3,1,1],[]]
 => 6
[1,2,1,1] => [2,1,1,1]
 => [[2,1,1,1],[]]
 => 4
[1,2,2] => [2,2,1]
 => [[2,2,1],[]]
 => 5
[1,3,1] => [3,1,1]
 => [[3,1,1],[]]
 => 6
[1,4] => [4,1]
 => [[4,1],[]]
 => 4
[2,1,1,1] => [2,1,1,1]
 => [[2,1,1,1],[]]
 => 4
[2,1,2] => [2,2,1]
 => [[2,2,1],[]]
 => 5
[2,2,1] => [2,2,1]
 => [[2,2,1],[]]
 => 5
[2,3] => [3,2]
 => [[3,2],[]]
 => 5
[3,1,1] => [3,1,1]
 => [[3,1,1],[]]
 => 6
[3,2] => [3,2]
 => [[3,2],[]]
 => 5
[4,1] => [4,1]
 => [[4,1],[]]
 => 4
[5] => [5]
 => [[5],[]]
 => 1
[1,1,1,1,1,1] => [1,1,1,1,1,1]
 => [[1,1,1,1,1,1],[]]
 => 1
[1,1,1,1,2] => [2,1,1,1,1]
 => [[2,1,1,1,1],[]]
 => 5
[1,1,1,2,1] => [2,1,1,1,1]
 => [[2,1,1,1,1],[]]
 => 5
[1,1,1,3] => [3,1,1,1]
 => [[3,1,1,1],[]]
 => 10
[1,1,2,1,1] => [2,1,1,1,1]
 => [[2,1,1,1,1],[]]
 => 5
[1,1,2,2] => [2,2,1,1]
 => [[2,2,1,1],[]]
 => 9
[1,1,3,1] => [3,1,1,1]
 => [[3,1,1,1],[]]
 => 10
[1,1,4] => [4,1,1]
 => [[4,1,1],[]]
 => 10
[1,2,1,1,1] => [2,1,1,1,1]
 => [[2,1,1,1,1],[]]
 => 5
[1,2,1,2] => [2,2,1,1]
 => [[2,2,1,1],[]]
 => 9
[1,2,2,1] => [2,2,1,1]
 => [[2,2,1,1],[]]
 => 9
[1,2,3] => [3,2,1]
 => [[3,2,1],[]]
 => 16
[1,3,1,1] => [3,1,1,1]
 => [[3,1,1,1],[]]
 => 10
[1,3,2] => [3,2,1]
 => [[3,2,1],[]]
 => 16
[1,4,1] => [4,1,1]
 => [[4,1,1],[]]
 => 10
[1,5] => [5,1]
 => [[5,1],[]]
 => 5
[2,1,1,1,1] => [2,1,1,1,1]
 => [[2,1,1,1,1],[]]
 => 5
[2,1,1,2] => [2,2,1,1]
 => [[2,2,1,1],[]]
 => 9
[2,1,2,1] => [2,2,1,1]
 => [[2,2,1,1],[]]
 => 9
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1]
 => [[1,1,1,1,1,1,1,1],[]]
 => ? = 1
[1,1,1,1,1,1,2] => [2,1,1,1,1,1,1]
 => [[2,1,1,1,1,1,1],[]]
 => ? = 7
[1,1,1,1,1,2,1] => [2,1,1,1,1,1,1]
 => [[2,1,1,1,1,1,1],[]]
 => ? = 7
[1,1,1,1,1,3] => [3,1,1,1,1,1]
 => [[3,1,1,1,1,1],[]]
 => ? = 21
[1,1,1,1,2,1,1] => [2,1,1,1,1,1,1]
 => [[2,1,1,1,1,1,1],[]]
 => ? = 7
[1,1,1,1,2,2] => [2,2,1,1,1,1]
 => [[2,2,1,1,1,1],[]]
 => ? = 20
[1,1,1,1,3,1] => [3,1,1,1,1,1]
 => [[3,1,1,1,1,1],[]]
 => ? = 21
[1,1,1,1,4] => [4,1,1,1,1]
 => [[4,1,1,1,1],[]]
 => ? = 35
[1,1,1,2,1,1,1] => [2,1,1,1,1,1,1]
 => [[2,1,1,1,1,1,1],[]]
 => ? = 7
[1,1,1,2,1,2] => [2,2,1,1,1,1]
 => [[2,2,1,1,1,1],[]]
 => ? = 20
[1,1,1,2,2,1] => [2,2,1,1,1,1]
 => [[2,2,1,1,1,1],[]]
 => ? = 20
[1,1,1,2,3] => [3,2,1,1,1]
 => [[3,2,1,1,1],[]]
 => ? = 64
[1,1,1,3,1,1] => [3,1,1,1,1,1]
 => [[3,1,1,1,1,1],[]]
 => ? = 21
[1,1,1,3,2] => [3,2,1,1,1]
 => [[3,2,1,1,1],[]]
 => ? = 64
[1,1,1,4,1] => [4,1,1,1,1]
 => [[4,1,1,1,1],[]]
 => ? = 35
[1,1,1,5] => [5,1,1,1]
 => [[5,1,1,1],[]]
 => ? = 35
[1,1,2,1,1,1,1] => [2,1,1,1,1,1,1]
 => [[2,1,1,1,1,1,1],[]]
 => ? = 7
[1,1,2,1,1,2] => [2,2,1,1,1,1]
 => [[2,2,1,1,1,1],[]]
 => ? = 20
[1,1,2,1,2,1] => [2,2,1,1,1,1]
 => [[2,2,1,1,1,1],[]]
 => ? = 20
[1,1,2,1,3] => [3,2,1,1,1]
 => [[3,2,1,1,1],[]]
 => ? = 64
[1,1,2,2,1,1] => [2,2,1,1,1,1]
 => [[2,2,1,1,1,1],[]]
 => ? = 20
[1,1,2,2,2] => [2,2,2,1,1]
 => [[2,2,2,1,1],[]]
 => ? = 28
[1,1,2,3,1] => [3,2,1,1,1]
 => [[3,2,1,1,1],[]]
 => ? = 64
[1,1,2,4] => [4,2,1,1]
 => [[4,2,1,1],[]]
 => ? = 90
[1,1,3,1,1,1] => [3,1,1,1,1,1]
 => [[3,1,1,1,1,1],[]]
 => ? = 21
[1,1,3,1,2] => [3,2,1,1,1]
 => [[3,2,1,1,1],[]]
 => ? = 64
[1,1,3,2,1] => [3,2,1,1,1]
 => [[3,2,1,1,1],[]]
 => ? = 64
[1,1,3,3] => [3,3,1,1]
 => [[3,3,1,1],[]]
 => ? = 56
[1,1,4,1,1] => [4,1,1,1,1]
 => [[4,1,1,1,1],[]]
 => ? = 35
[1,1,4,2] => [4,2,1,1]
 => [[4,2,1,1],[]]
 => ? = 90
[1,1,5,1] => [5,1,1,1]
 => [[5,1,1,1],[]]
 => ? = 35
[1,1,6] => [6,1,1]
 => [[6,1,1],[]]
 => ? = 21
[1,2,1,1,1,1,1] => [2,1,1,1,1,1,1]
 => [[2,1,1,1,1,1,1],[]]
 => ? = 7
[1,2,1,1,1,2] => [2,2,1,1,1,1]
 => [[2,2,1,1,1,1],[]]
 => ? = 20
[1,2,1,1,2,1] => [2,2,1,1,1,1]
 => [[2,2,1,1,1,1],[]]
 => ? = 20
[1,2,1,1,3] => [3,2,1,1,1]
 => [[3,2,1,1,1],[]]
 => ? = 64
[1,2,1,2,1,1] => [2,2,1,1,1,1]
 => [[2,2,1,1,1,1],[]]
 => ? = 20
[1,2,1,2,2] => [2,2,2,1,1]
 => [[2,2,2,1,1],[]]
 => ? = 28
[1,2,1,3,1] => [3,2,1,1,1]
 => [[3,2,1,1,1],[]]
 => ? = 64
[1,2,1,4] => [4,2,1,1]
 => [[4,2,1,1],[]]
 => ? = 90
[1,2,2,1,1,1] => [2,2,1,1,1,1]
 => [[2,2,1,1,1,1],[]]
 => ? = 20
[1,2,2,1,2] => [2,2,2,1,1]
 => [[2,2,2,1,1],[]]
 => ? = 28
[1,2,2,2,1] => [2,2,2,1,1]
 => [[2,2,2,1,1],[]]
 => ? = 28
[1,2,2,3] => [3,2,2,1]
 => [[3,2,2,1],[]]
 => ? = 70
[1,2,3,1,1] => [3,2,1,1,1]
 => [[3,2,1,1,1],[]]
 => ? = 64
[1,2,3,2] => [3,2,2,1]
 => [[3,2,2,1],[]]
 => ? = 70
[1,2,4,1] => [4,2,1,1]
 => [[4,2,1,1],[]]
 => ? = 90
[1,2,5] => [5,2,1]
 => [[5,2,1],[]]
 => ? = 64
[1,3,1,1,1,1] => [3,1,1,1,1,1]
 => [[3,1,1,1,1,1],[]]
 => ? = 21
[1,3,1,1,2] => [3,2,1,1,1]
 => [[3,2,1,1,1],[]]
 => ? = 64
Description
The number of standard Young tableaux of the skew partition.