Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001908
Mapping
St001908: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 1
[1,1]
 => 1
[3]
 => 1
[2,1]
 => 2
[1,1,1]
 => 1
[4]
 => 1
[3,1]
 => 3
[2,2]
 => 1
[2,1,1]
 => 3
[1,1,1,1]
 => 1
[5]
 => 1
[4,1]
 => 4
[3,2]
 => 2
[3,1,1]
 => 6
[2,2,1]
 => 3
[2,1,1,1]
 => 4
[1,1,1,1,1]
 => 1
[6]
 => 1
[5,1]
 => 5
[4,2]
 => 3
[4,1,1]
 => 10
[3,3]
 => 1
[3,2,1]
 => 7
[3,1,1,1]
 => 10
[2,2,2]
 => 1
[2,2,1,1]
 => 6
[2,1,1,1,1]
 => 5
[1,1,1,1,1,1]
 => 1
[7]
 => 1
[6,1]
 => 6
[5,2]
 => 4
[5,1,1]
 => 15
[4,3]
 => 2
[4,2,1]
 => 12
[4,1,1,1]
 => 20
[3,3,1]
 => 6
[3,2,2]
 => 3
[3,2,1,1]
 => 16
[3,1,1,1,1]
 => 15
[2,2,2,1]
 => 4
[2,2,1,1,1]
 => 10
[2,1,1,1,1,1]
 => 6
[1,1,1,1,1,1,1]
 => 1
[8]
 => 1
[7,1]
 => 7
[6,2]
 => 5
[6,1,1]
 => 21
[5,3]
 => 3
[5,2,1]
 => 18
Description
The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. For example, there are eight tableaux of shape $[3,2,1]$ with maximal entry $3$, but two of them have the same weight.
Matching statistic: St000220
Mapping
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St000220: Permutations ⟶ ℤResult quality: 4% ●values known / values provided: 7%●distinct values known / distinct values provided: 4%
Values
[1]
 => [1,0]
 => [1,1,0,0]
 => [2,3,1] => 0 = 1 - 1
[2]
 => [1,0,1,0]
 => [1,1,0,1,0,0]
 => [4,3,1,2] => 0 = 1 - 1
[1,1]
 => [1,1,0,0]
 => [1,1,1,0,0,0]
 => [2,3,4,1] => 0 = 1 - 1
[3]
 => [1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [5,4,1,2,3] => 0 = 1 - 1
[2,1]
 => [1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [4,3,1,5,2] => 1 = 2 - 1
[1,1,1]
 => [1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => [5,3,4,1,2] => 0 = 1 - 1
[4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [5,6,1,2,3,4] => 0 = 1 - 1
[3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [5,4,1,2,6,3] => 2 = 3 - 1
[2,2]
 => [1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => 0 = 1 - 1
[2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [6,4,1,5,2,3] => 2 = 3 - 1
[1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [6,5,4,1,2,3] => 0 = 1 - 1
[5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [7,6,1,2,3,4,5] => 0 = 1 - 1
[4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => [5,6,1,2,3,7,4] => 3 = 4 - 1
[3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [4,3,1,5,6,2] => 2 = 3 - 1
[3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,0,0]
 => [5,7,1,2,6,3,4] => ? ∊ {1,2,4} - 1
[2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [2,6,4,5,1,3] => 5 = 6 - 1
[2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => [6,7,1,5,2,3,4] => ? ∊ {1,2,4} - 1
[1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [6,7,5,1,2,3,4] => ? ∊ {1,2,4} - 1
[6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [8,7,1,2,3,4,5,6] => 0 = 1 - 1
[5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
 => [7,6,1,2,3,4,8,5] => ? ∊ {3,5,5,6,7,10,10} - 1
[4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [5,4,1,2,6,7,3] => ? ∊ {3,5,5,6,7,10,10} - 1
[4,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
 => [8,6,1,2,3,7,4,5] => ? ∊ {3,5,5,6,7,10,10} - 1
[3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [6,3,4,5,1,2] => 0 = 1 - 1
[3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => [7,3,1,5,6,2,4] => ? ∊ {3,5,5,6,7,10,10} - 1
[3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => [8,7,1,2,6,3,4,5] => ? ∊ {3,5,5,6,7,10,10} - 1
[2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [2,3,4,5,6,1] => 0 = 1 - 1
[2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => [2,7,6,5,1,3,4] => ? ∊ {3,5,5,6,7,10,10} - 1
[2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => [8,7,1,6,2,3,4,5] => ? ∊ {3,5,5,6,7,10,10} - 1
[1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
 => [6,7,8,1,2,3,4,5] => 0 = 1 - 1
[7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [8,9,1,2,3,4,5,6,7] => 0 = 1 - 1
[6,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
 => [8,7,1,2,3,4,5,9,6] => ? ∊ {2,3,4,4,6,6,6,10,12,15,15,16,20} - 1
[5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,1,1,1,0,0,0,0]
 => [5,6,1,2,3,7,8,4] => ? ∊ {2,3,4,4,6,6,6,10,12,15,15,16,20} - 1
[5,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
 => [9,7,1,2,3,4,8,5,6] => ? ∊ {2,3,4,4,6,6,6,10,12,15,15,16,20} - 1
[4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => [7,4,1,5,6,2,3] => ? ∊ {2,3,4,4,6,6,6,10,12,15,15,16,20} - 1
[4,2,1]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,1,1,1,0,0,1,0,0,0]
 => [8,4,1,2,6,7,3,5] => ? ∊ {2,3,4,4,6,6,6,10,12,15,15,16,20} - 1
[4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => [9,8,1,2,3,7,4,5,6] => ? ∊ {2,3,4,4,6,6,6,10,12,15,15,16,20} - 1
[3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,1,0,1,0,0,1,0,0,0]
 => [7,3,6,5,1,2,4] => ? ∊ {2,3,4,4,6,6,6,10,12,15,15,16,20} - 1
[3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [4,3,1,5,6,7,2] => ? ∊ {2,3,4,4,6,6,6,10,12,15,15,16,20} - 1
[3,2,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,1,0,0,0]
 => [8,3,1,7,6,2,4,5] => ? ∊ {2,3,4,4,6,6,6,10,12,15,15,16,20} - 1
[3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => [9,8,1,2,7,3,4,5,6] => ? ∊ {2,3,4,4,6,6,6,10,12,15,15,16,20} - 1
[2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => [2,3,7,5,6,1,4] => ? ∊ {2,3,4,4,6,6,6,10,12,15,15,16,20} - 1
[2,2,1,1,1]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,1,0,0,0]
 => [2,7,8,6,1,3,4,5] => ? ∊ {2,3,4,4,6,6,6,10,12,15,15,16,20} - 1
[2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
 => [8,7,1,9,2,3,4,5,6] => ? ∊ {2,3,4,4,6,6,6,10,12,15,15,16,20} - 1
[1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
 => [9,7,8,1,2,3,4,5,6] => 0 = 1 - 1
[8]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [10,9,1,2,3,4,5,6,7,8] => 0 = 1 - 1
[7,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
 => [8,9,1,2,3,4,5,6,10,7] => ? ∊ {1,3,3,5,6,7,7,10,12,13,15,18,19,21,21,30,31,35,35} - 1
[6,2]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
 => [7,6,1,2,3,4,8,9,5] => ? ∊ {1,3,3,5,6,7,7,10,12,13,15,18,19,21,21,30,31,35,35} - 1
[6,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
 => [8,10,1,2,3,4,5,9,6,7] => ? ∊ {1,3,3,5,6,7,7,10,12,13,15,18,19,21,21,30,31,35,35} - 1
[5,3]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,1,0,0,0,0]
 => [5,8,1,2,6,7,3,4] => ? ∊ {1,3,3,5,6,7,7,10,12,13,15,18,19,21,21,30,31,35,35} - 1
[5,2,1]
 => [1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
 => [5,9,1,2,3,7,8,4,6] => ? ∊ {1,3,3,5,6,7,7,10,12,13,15,18,19,21,21,30,31,35,35} - 1
[5,1,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => [9,10,1,2,3,4,8,5,6,7] => ? ∊ {1,3,3,5,6,7,7,10,12,13,15,18,19,21,21,30,31,35,35} - 1
[4,4]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => [7,6,4,5,1,2,3] => 0 = 1 - 1
[4,3,1]
 => [1,0,1,1,1,0,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,1,0,0,1,0,0,0]
 => [8,4,1,7,6,2,3,5] => ? ∊ {1,3,3,5,6,7,7,10,12,13,15,18,19,21,21,30,31,35,35} - 1
[4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,1,1,1,0,0,0,0,0]
 => [5,4,1,2,6,7,8,3] => ? ∊ {1,3,3,5,6,7,7,10,12,13,15,18,19,21,21,30,31,35,35} - 1
[4,2,1,1]
 => [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
 => [9,4,1,2,8,7,3,5,6] => ? ∊ {1,3,3,5,6,7,7,10,12,13,15,18,19,21,21,30,31,35,35} - 1
[4,1,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => [9,10,1,2,3,8,4,5,6,7] => ? ∊ {1,3,3,5,6,7,7,10,12,13,15,18,19,21,21,30,31,35,35} - 1
[3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => [6,3,4,5,1,7,2] => ? ∊ {1,3,3,5,6,7,7,10,12,13,15,18,19,21,21,30,31,35,35} - 1
[3,3,1,1]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,1,0,0,1,0,1,0,0,0]
 => [7,3,8,6,1,2,4,5] => ? ∊ {1,3,3,5,6,7,7,10,12,13,15,18,19,21,21,30,31,35,35} - 1
[3,2,2,1]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,1,1,1,0,0,0,1,0,0,0]
 => [4,3,1,8,6,7,2,5] => ? ∊ {1,3,3,5,6,7,7,10,12,13,15,18,19,21,21,30,31,35,35} - 1
[3,2,1,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
 => [8,3,1,9,7,2,4,5,6] => ? ∊ {1,3,3,5,6,7,7,10,12,13,15,18,19,21,21,30,31,35,35} - 1
[3,1,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
 => [9,8,1,2,10,3,4,5,6,7] => ? ∊ {1,3,3,5,6,7,7,10,12,13,15,18,19,21,21,30,31,35,35} - 1
[2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => [7,3,4,5,6,1,2] => ? ∊ {1,3,3,5,6,7,7,10,12,13,15,18,19,21,21,30,31,35,35} - 1
[2,2,2,1,1]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => [2,3,8,7,6,1,4,5] => ? ∊ {1,3,3,5,6,7,7,10,12,13,15,18,19,21,21,30,31,35,35} - 1
[2,2,1,1,1,1]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
 => [2,7,8,9,1,3,4,5,6] => ? ∊ {1,3,3,5,6,7,7,10,12,13,15,18,19,21,21,30,31,35,35} - 1
[2,1,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
 => [10,8,1,9,2,3,4,5,6,7] => ? ∊ {1,3,3,5,6,7,7,10,12,13,15,18,19,21,21,30,31,35,35} - 1
[1,1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
 => [10,9,8,1,2,3,4,5,6,7] => 0 = 1 - 1
[9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [11,10,1,2,3,4,5,6,7,8,9] => ? ∊ {1,1,2,4,4,5,6,7,8,8,10,10,16,19,20,21,25,28,28,28,35,40,45,50,52,56,56,65,70} - 1
[8,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
 => [10,9,1,2,3,4,5,6,7,11,8] => ? ∊ {1,1,2,4,4,5,6,7,8,8,10,10,16,19,20,21,25,28,28,28,35,40,45,50,52,56,56,65,70} - 1
[7,2]
 => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
 => [8,7,1,2,3,4,5,9,10,6] => ? ∊ {1,1,2,4,4,5,6,7,8,8,10,10,16,19,20,21,25,28,28,28,35,40,45,50,52,56,56,65,70} - 1
[7,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
 => [11,9,1,2,3,4,5,6,10,7,8] => ? ∊ {1,1,2,4,4,5,6,7,8,8,10,10,16,19,20,21,25,28,28,28,35,40,45,50,52,56,56,65,70} - 1
[6,3]
 => [1,0,1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
 => [9,6,1,2,3,7,8,4,5] => ? ∊ {1,1,2,4,4,5,6,7,8,8,10,10,16,19,20,21,25,28,28,28,35,40,45,50,52,56,56,65,70} - 1
[6,2,1]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
 => [10,6,1,2,3,4,8,9,5,7] => ? ∊ {1,1,2,4,4,5,6,7,8,8,10,10,16,19,20,21,25,28,28,28,35,40,45,50,52,56,56,65,70} - 1
[6,1,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => [11,10,1,2,3,4,5,9,6,7,8] => ? ∊ {1,1,2,4,4,5,6,7,8,8,10,10,16,19,20,21,25,28,28,28,35,40,45,50,52,56,56,65,70} - 1
[5,4]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,1,0,0,0,0]
 => [7,8,1,5,6,2,3,4] => ? ∊ {1,1,2,4,4,5,6,7,8,8,10,10,16,19,20,21,25,28,28,28,35,40,45,50,52,56,56,65,70} - 1
[3,3,3]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [2,3,4,5,6,7,1] => 0 = 1 - 1
[2,2,2,2,2]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
 => [8,7,4,5,6,1,2,3] => 0 = 1 - 1
[3,3,3,3]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [2,3,4,5,6,7,8,1] => 0 = 1 - 1
Description
The number of occurrences of the pattern 132 in a permutation.