Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St000075
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Mapping
St000075: Standard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => 1
[[1,2]]
 => 1
[[1],[2]]
 => 1
[[1,2,3]]
 => 1
[[1,3],[2]]
 => 2
[[1,2],[3]]
 => 2
[[1],[2],[3]]
 => 1
[[1,2,3,4]]
 => 1
[[1,3,4],[2]]
 => 3
[[1,2,4],[3]]
 => 3
[[1,2,3],[4]]
 => 3
[[1,3],[2,4]]
 => 2
[[1,2],[3,4]]
 => 2
[[1,4],[2],[3]]
 => 3
[[1,3],[2],[4]]
 => 3
[[1,2],[3],[4]]
 => 3
[[1],[2],[3],[4]]
 => 1
[[1,2,3,4,5]]
 => 1
[[1,3,4,5],[2]]
 => 4
[[1,2,4,5],[3]]
 => 4
[[1,2,3,5],[4]]
 => 4
[[1,2,3,4],[5]]
 => 4
[[1,3,5],[2,4]]
 => 2
[[1,2,5],[3,4]]
 => 3
[[1,3,4],[2,5]]
 => 3
[[1,2,4],[3,5]]
 => 2
[[1,2,3],[4,5]]
 => 3
[[1,4,5],[2],[3]]
 => 4
[[1,3,5],[2],[4]]
 => 2
[[1,2,5],[3],[4]]
 => 4
[[1,3,4],[2],[5]]
 => 4
[[1,2,4],[3],[5]]
 => 2
[[1,2,3],[4],[5]]
 => 4
[[1,4],[2,5],[3]]
 => 3
[[1,3],[2,5],[4]]
 => 2
[[1,2],[3,5],[4]]
 => 3
[[1,3],[2,4],[5]]
 => 3
[[1,2],[3,4],[5]]
 => 2
[[1,5],[2],[3],[4]]
 => 4
[[1,4],[2],[3],[5]]
 => 4
[[1,3],[2],[4],[5]]
 => 4
[[1,2],[3],[4],[5]]
 => 4
[[1],[2],[3],[4],[5]]
 => 1
[[1,2,3,4,5,6]]
 => 1
[[1,3,4,5,6],[2]]
 => 5
[[1,2,4,5,6],[3]]
 => 5
[[1,2,3,5,6],[4]]
 => 5
[[1,2,3,4,6],[5]]
 => 5
[[1,2,3,4,5],[6]]
 => 5
[[1,3,5,6],[2,4]]
 => 5
Description
The orbit size of a standard tableau under promotion.
Matching statistic: St001633
Mapping
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001633: Posets ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 50%
Values
[[1]]
 => [1] => [1] => ([],1)
 => 0 = 1 - 1
[[1,2]]
 => [1,2] => [1,2] => ([(0,1)],2)
 => 0 = 1 - 1
[[1],[2]]
 => [2,1] => [2,1] => ([(0,1)],2)
 => 0 = 1 - 1
[[1,2,3]]
 => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
 => 0 = 1 - 1
[[1,3],[2]]
 => [2,1,3] => [2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
[[1,2],[3]]
 => [3,1,2] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
[[1],[2],[3]]
 => [3,2,1] => [3,2,1] => ([(0,2),(2,1)],3)
 => 0 = 1 - 1
[[1,2,3,4]]
 => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 0 = 1 - 1
[[1,3,4],[2]]
 => [2,1,3,4] => [2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2 = 3 - 1
[[1,2,4],[3]]
 => [3,1,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
 => ? = 3 - 1
[[1,2,3],[4]]
 => [4,1,2,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2 = 3 - 1
[[1,3],[2,4]]
 => [2,4,1,3] => [4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
 => ? = 2 - 1
[[1,2],[3,4]]
 => [3,4,1,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
 => ? = 2 - 1
[[1,4],[2],[3]]
 => [3,2,1,4] => [3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2 = 3 - 1
[[1,3],[2],[4]]
 => [4,2,1,3] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => 2 = 3 - 1
[[1,2],[3],[4]]
 => [4,3,1,2] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 2 = 3 - 1
[[1],[2],[3],[4]]
 => [4,3,2,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
 => 0 = 1 - 1
[[1,2,3,4,5]]
 => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0 = 1 - 1
[[1,3,4,5],[2]]
 => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 4 - 1
[[1,2,4,5],[3]]
 => [3,1,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 4 - 1
[[1,2,3,5],[4]]
 => [4,1,2,3,5] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 4 - 1
[[1,2,3,4],[5]]
 => [5,1,2,3,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 4 - 1
[[1,3,5],[2,4]]
 => [2,4,1,3,5] => [4,2,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => ? = 2 - 1
[[1,2,5],[3,4]]
 => [3,4,1,2,5] => [3,1,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
 => ? = 3 - 1
[[1,3,4],[2,5]]
 => [2,5,1,3,4] => [2,1,5,3,4] => ([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
 => ? = 3 - 1
[[1,2,4],[3,5]]
 => [3,5,1,2,4] => [1,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
 => ? = 2 - 1
[[1,2,3],[4,5]]
 => [4,5,1,2,3] => [1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
 => ? = 3 - 1
[[1,4,5],[2],[3]]
 => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 4 - 1
[[1,3,5],[2],[4]]
 => [4,2,1,3,5] => [2,1,4,3,5] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
 => ? = 2 - 1
[[1,2,5],[3],[4]]
 => [4,3,1,2,5] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
 => ? = 4 - 1
[[1,3,4],[2],[5]]
 => [5,2,1,3,4] => [2,1,3,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
 => ? = 4 - 1
[[1,2,4],[3],[5]]
 => [5,3,1,2,4] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
 => ? = 2 - 1
[[1,2,3],[4],[5]]
 => [5,4,1,2,3] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 4 - 1
[[1,4],[2,5],[3]]
 => [3,2,5,1,4] => [3,5,2,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
 => ? = 3 - 1
[[1,3],[2,5],[4]]
 => [4,2,5,1,3] => [2,4,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
 => ? = 2 - 1
[[1,2],[3,5],[4]]
 => [4,3,5,1,2] => [4,3,1,5,2] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
 => ? = 3 - 1
[[1,3],[2,4],[5]]
 => [5,2,4,1,3] => [5,2,1,4,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
 => ? = 3 - 1
[[1,2],[3,4],[5]]
 => [5,3,4,1,2] => [3,1,5,4,2] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
 => ? = 2 - 1
[[1,5],[2],[3],[4]]
 => [4,3,2,1,5] => [4,3,2,1,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 4 - 1
[[1,4],[2],[3],[5]]
 => [5,3,2,1,4] => [3,2,1,5,4] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
 => ? = 4 - 1
[[1,3],[2],[4],[5]]
 => [5,4,2,1,3] => [2,1,5,4,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
 => ? = 4 - 1
[[1,2],[3],[4],[5]]
 => [5,4,3,1,2] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 4 - 1
[[1],[2],[3],[4],[5]]
 => [5,4,3,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0 = 1 - 1
[[1,2,3,4,5,6]]
 => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[[1,3,4,5,6],[2]]
 => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
 => ? = 5 - 1
[[1,2,4,5,6],[3]]
 => [3,1,2,4,5,6] => [1,3,2,4,5,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 5 - 1
[[1,2,3,5,6],[4]]
 => [4,1,2,3,5,6] => [1,2,4,3,5,6] => ([(0,3),(0,4),(0,5),(1,9),(1,13),(2,8),(2,13),(3,11),(4,2),(4,6),(4,11),(5,1),(5,6),(5,11),(6,8),(6,9),(6,13),(8,10),(8,12),(9,10),(9,12),(10,7),(11,13),(12,7),(13,12)],14)
 => ? = 5 - 1
[[1,2,3,4,6],[5]]
 => [5,1,2,3,4,6] => [1,2,3,5,4,6] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 5 - 1
[[1,2,3,4,5],[6]]
 => [6,1,2,3,4,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
 => ? = 5 - 1
[[1,3,5,6],[2,4]]
 => [2,4,1,3,5,6] => [4,2,1,3,5,6] => ([(0,1),(0,2),(0,4),(0,5),(1,9),(1,16),(2,10),(2,16),(3,6),(3,7),(3,15),(4,9),(4,11),(4,16),(5,3),(5,10),(5,11),(5,16),(6,13),(7,13),(7,14),(9,12),(10,6),(10,15),(11,7),(11,12),(11,15),(12,14),(13,8),(14,8),(15,13),(15,14),(16,12),(16,15)],17)
 => ? = 5 - 1
[[1,2,5,6],[3,4]]
 => [3,4,1,2,5,6] => [3,1,4,2,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
 => ? = 4 - 1
[[1,3,4,6],[2,5]]
 => [2,5,1,3,4,6] => [2,1,5,3,4,6] => ([(0,2),(0,3),(0,4),(0,5),(1,10),(1,15),(1,17),(2,7),(2,13),(3,8),(3,9),(3,13),(4,8),(4,11),(4,13),(5,1),(5,7),(5,9),(5,11),(7,17),(8,12),(8,15),(9,12),(9,15),(9,17),(10,14),(10,16),(11,10),(11,12),(11,17),(12,14),(12,16),(13,15),(13,17),(14,6),(15,14),(15,16),(16,6),(17,16)],18)
 => ? = 5 - 1
[[1,2,4,6],[3,5]]
 => [3,5,1,2,4,6] => [1,5,3,2,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(1,13),(1,17),(2,10),(2,11),(2,17),(3,8),(3,9),(3,13),(3,17),(4,7),(4,9),(4,10),(4,17),(5,7),(5,8),(5,11),(5,12),(7,15),(7,20),(7,21),(8,14),(8,15),(8,20),(9,15),(9,16),(9,21),(10,21),(11,20),(11,21),(12,14),(12,20),(13,14),(13,16),(14,19),(15,18),(15,19),(16,18),(16,19),(17,16),(17,20),(17,21),(18,6),(19,6),(20,18),(20,19),(21,18)],22)
 => ? = 5 - 1
[[1,2,3,6],[4,5]]
 => [4,5,1,2,3,6] => [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(1,17),(1,22),(2,13),(2,17),(2,22),(3,9),(3,11),(3,17),(3,22),(4,8),(4,10),(4,17),(4,22),(5,8),(5,9),(5,12),(5,13),(5,22),(6,10),(6,11),(6,12),(6,14),(6,22),(8,15),(8,19),(8,23),(9,16),(9,19),(9,23),(10,15),(10,20),(10,23),(11,16),(11,20),(11,23),(12,15),(12,16),(12,19),(12,20),(13,19),(13,23),(14,20),(14,23),(15,18),(15,21),(16,18),(16,21),(17,23),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,19),(22,20),(22,23),(23,21)],24)
 => ? = 4 - 1
[[1,3,4,5],[2,6]]
 => [2,6,1,3,4,5] => [2,1,3,6,4,5] => ([(0,2),(0,3),(0,4),(0,5),(1,13),(1,16),(2,6),(2,14),(3,10),(3,11),(3,14),(4,9),(4,11),(4,14),(5,6),(5,9),(5,10),(6,15),(7,13),(7,16),(9,12),(9,15),(10,1),(10,12),(10,15),(11,7),(11,12),(12,13),(12,16),(13,8),(14,7),(14,15),(15,16),(16,8)],17)
 => ? = 4 - 1
[[1,2,4,5],[3,6]]
 => [3,6,1,2,4,5] => [1,3,2,6,4,5] => ([(0,2),(0,3),(0,4),(0,5),(1,14),(1,16),(2,7),(2,8),(2,9),(3,7),(3,10),(3,12),(4,8),(4,11),(4,12),(5,9),(5,10),(5,11),(7,17),(8,15),(8,17),(9,1),(9,15),(9,17),(10,13),(10,17),(11,13),(11,15),(12,13),(12,15),(12,17),(13,14),(13,16),(14,6),(15,14),(15,16),(16,6),(17,16)],18)
 => ? = 5 - 1
[[1,2,3,5],[4,6]]
 => [4,6,1,2,3,5] => [1,2,6,4,3,5] => ([(0,1),(0,2),(0,3),(0,5),(1,11),(1,14),(2,10),(2,13),(2,14),(3,10),(3,12),(3,14),(4,7),(4,8),(4,9),(5,4),(5,11),(5,12),(5,13),(7,17),(8,17),(8,18),(9,17),(9,18),(10,15),(11,7),(11,16),(12,8),(12,15),(12,16),(13,9),(13,15),(13,16),(14,15),(14,16),(15,18),(16,17),(16,18),(17,6),(18,6)],19)
 => ? = 5 - 1
[[1,2,3,4],[5,6]]
 => [5,6,1,2,3,4] => [1,2,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,14),(1,18),(2,13),(2,14),(2,18),(3,12),(3,14),(3,18),(4,11),(4,14),(4,18),(5,8),(5,9),(5,10),(5,16),(6,5),(6,11),(6,12),(6,13),(6,18),(8,15),(8,19),(9,15),(9,19),(10,15),(10,19),(11,8),(11,16),(11,17),(12,9),(12,16),(12,17),(13,10),(13,16),(13,17),(14,17),(15,7),(16,15),(16,19),(17,19),(18,16),(18,17),(19,7)],20)
 => ? = 4 - 1
[[1,4,5,6],[2],[3]]
 => [3,2,1,4,5,6] => [3,2,1,4,5,6] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
 => ? = 5 - 1
[[1,3,5,6],[2],[4]]
 => [4,2,1,3,5,6] => [2,1,4,3,5,6] => ([(0,2),(0,3),(0,4),(1,7),(1,13),(2,6),(2,12),(3,1),(3,9),(3,12),(4,6),(4,9),(4,12),(6,10),(7,8),(7,11),(8,5),(9,7),(9,10),(9,13),(10,11),(11,5),(12,10),(12,13),(13,8),(13,11)],14)
 => ? = 5 - 1
[[1,2,5,6],[3],[4]]
 => [4,3,1,2,5,6] => [1,4,3,2,5,6] => ([(0,3),(0,4),(0,5),(1,13),(2,6),(2,8),(3,9),(3,10),(4,2),(4,10),(4,11),(5,1),(5,9),(5,11),(6,14),(6,15),(8,14),(9,12),(9,13),(10,8),(10,12),(11,6),(11,12),(11,13),(12,14),(12,15),(13,15),(14,7),(15,7)],16)
 => ? = 5 - 1
[[1,3,4,6],[2],[5]]
 => [5,2,1,3,4,6] => [2,1,3,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,13),(2,8),(2,9),(2,13),(3,7),(3,9),(3,13),(4,6),(4,7),(4,8),(6,15),(7,12),(7,15),(8,11),(8,12),(8,15),(9,11),(9,12),(10,5),(11,10),(11,14),(12,10),(12,14),(13,11),(13,15),(14,5),(15,14)],16)
 => ? = 5 - 1
[[1,2,4,6],[3],[5]]
 => [5,3,1,2,4,6] => [1,3,2,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,15),(2,7),(2,9),(2,15),(3,6),(3,7),(3,15),(4,6),(4,8),(4,15),(6,14),(7,11),(7,14),(8,12),(8,14),(9,11),(9,12),(10,5),(11,10),(11,13),(12,10),(12,13),(13,5),(14,13),(15,11),(15,12),(15,14)],16)
 => ? = 5 - 1
[[1,2,3,6],[4],[5]]
 => [5,4,1,2,3,6] => [1,2,5,4,3,6] => ([(0,3),(0,4),(0,5),(1,13),(2,6),(2,8),(3,9),(3,10),(4,2),(4,10),(4,11),(5,1),(5,9),(5,11),(6,14),(6,15),(8,14),(9,12),(9,13),(10,8),(10,12),(11,6),(11,12),(11,13),(12,14),(12,15),(13,15),(14,7),(15,7)],16)
 => ? = 5 - 1
[[1,3,4,5],[2],[6]]
 => [6,2,1,3,4,5] => [2,1,3,4,6,5] => ([(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,11),(3,6),(3,10),(4,1),(4,10),(4,11),(6,12),(7,9),(7,13),(8,9),(8,13),(9,5),(10,7),(10,12),(11,8),(11,12),(12,13),(13,5)],14)
 => ? = 5 - 1
[[1,2,4,5],[3],[6]]
 => [6,3,1,2,4,5] => [1,3,2,4,6,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,13),(2,8),(2,9),(2,13),(3,7),(3,9),(3,13),(4,6),(4,7),(4,8),(6,15),(7,12),(7,15),(8,11),(8,12),(8,15),(9,11),(9,12),(10,5),(11,10),(11,14),(12,10),(12,14),(13,11),(13,15),(14,5),(15,14)],16)
 => ? = 5 - 1
[[1,2,3,5],[4],[6]]
 => [6,4,1,2,3,5] => [1,2,4,3,6,5] => ([(0,2),(0,3),(0,4),(1,7),(1,13),(2,6),(2,12),(3,1),(3,9),(3,12),(4,6),(4,9),(4,12),(6,10),(7,8),(7,11),(8,5),(9,7),(9,10),(9,13),(10,11),(11,5),(12,10),(12,13),(13,8),(13,11)],14)
 => ? = 5 - 1
[[1],[2],[3],[4],[5],[6]]
 => [6,5,4,3,2,1] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[[1,2,3,4,5,6,7]]
 => [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)
 => 0 = 1 - 1
Description
The number of simple modules with projective dimension two in the incidence algebra of the poset.
Matching statistic: St001686
(load all 24 compositions to match this statistic)
Mapping
Mp00082: Standard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
St001686: Gelfand-Tsetlin patterns ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 50%
Values
[[1]]
 => [[1]]
 => ? = 1
[[1,2]]
 => [[2,0],[1]]
 => 1
[[1],[2]]
 => [[1,1],[1]]
 => 1
[[1,2,3]]
 => [[3,0,0],[2,0],[1]]
 => 1
[[1,3],[2]]
 => [[2,1,0],[1,1],[1]]
 => 2
[[1,2],[3]]
 => [[2,1,0],[2,0],[1]]
 => 2
[[1],[2],[3]]
 => [[1,1,1],[1,1],[1]]
 => 1
[[1,2,3,4]]
 => [[4,0,0,0],[3,0,0],[2,0],[1]]
 => 1
[[1,3,4],[2]]
 => [[3,1,0,0],[2,1,0],[1,1],[1]]
 => 3
[[1,2,4],[3]]
 => [[3,1,0,0],[2,1,0],[2,0],[1]]
 => 3
[[1,2,3],[4]]
 => [[3,1,0,0],[3,0,0],[2,0],[1]]
 => 3
[[1,3],[2,4]]
 => [[2,2,0,0],[2,1,0],[1,1],[1]]
 => 2
[[1,2],[3,4]]
 => [[2,2,0,0],[2,1,0],[2,0],[1]]
 => 2
[[1,4],[2],[3]]
 => [[2,1,1,0],[1,1,1],[1,1],[1]]
 => 3
[[1,3],[2],[4]]
 => [[2,1,1,0],[2,1,0],[1,1],[1]]
 => 3
[[1,2],[3],[4]]
 => [[2,1,1,0],[2,1,0],[2,0],[1]]
 => 3
[[1],[2],[3],[4]]
 => [[1,1,1,1],[1,1,1],[1,1],[1]]
 => 1
[[1,2,3,4,5]]
 => [[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => ? = 1
[[1,3,4,5],[2]]
 => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => ? = 4
[[1,2,4,5],[3]]
 => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => ? = 4
[[1,2,3,5],[4]]
 => [[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => ? = 4
[[1,2,3,4],[5]]
 => [[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => ? = 4
[[1,3,5],[2,4]]
 => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
 => ? = 2
[[1,2,5],[3,4]]
 => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
 => ? = 3
[[1,3,4],[2,5]]
 => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => ? = 3
[[1,2,4],[3,5]]
 => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => ? = 2
[[1,2,3],[4,5]]
 => [[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => ? = 3
[[1,4,5],[2],[3]]
 => [[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
 => ? = 4
[[1,3,5],[2],[4]]
 => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
 => ? = 2
[[1,2,5],[3],[4]]
 => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
 => ? = 4
[[1,3,4],[2],[5]]
 => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => ? = 4
[[1,2,4],[3],[5]]
 => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => ? = 2
[[1,2,3],[4],[5]]
 => [[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => ? = 4
[[1,4],[2,5],[3]]
 => [[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
 => ? = 3
[[1,3],[2,5],[4]]
 => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
 => ? = 2
[[1,2],[3,5],[4]]
 => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
 => ? = 3
[[1,3],[2,4],[5]]
 => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
 => ? = 3
[[1,2],[3,4],[5]]
 => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
 => ? = 2
[[1,5],[2],[3],[4]]
 => [[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
 => ? = 4
[[1,4],[2],[3],[5]]
 => [[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
 => ? = 4
[[1,3],[2],[4],[5]]
 => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
 => ? = 4
[[1,2],[3],[4],[5]]
 => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
 => ? = 4
[[1],[2],[3],[4],[5]]
 => [[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
 => ? = 1
[[1,2,3,4,5,6]]
 => [[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => ? = 1
[[1,3,4,5,6],[2]]
 => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => ? = 5
[[1,2,4,5,6],[3]]
 => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => ? = 5
[[1,2,3,5,6],[4]]
 => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => ? = 5
[[1,2,3,4,6],[5]]
 => [[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => ? = 5
[[1,2,3,4,5],[6]]
 => [[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => ? = 5
[[1,3,5,6],[2,4]]
 => [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
 => ? = 5
[[1,2,5,6],[3,4]]
 => [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
 => ? = 4
[[1,3,4,6],[2,5]]
 => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => ? = 5
[[1,2,4,6],[3,5]]
 => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => ? = 5
[[1,2,3,6],[4,5]]
 => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => ? = 4
[[1,3,4,5],[2,6]]
 => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => ? = 4
[[1,2,4,5],[3,6]]
 => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => ? = 5
[[1,2,3,5],[4,6]]
 => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => ? = 5
[[1,2,3,4],[5,6]]
 => [[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
 => ? = 4
[[1,4,5,6],[2],[3]]
 => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
 => ? = 5
[[1,3,5,6],[2],[4]]
 => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
 => ? = 5
[[1,2,5,6],[3],[4]]
 => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
 => ? = 5
[[1,3,4,6],[2],[5]]
 => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => ? = 5
[[1,2,4,6],[3],[5]]
 => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => ? = 5
[[1,2,3,6],[4],[5]]
 => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
 => ? = 5
[[1,3,4,5],[2],[6]]
 => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
 => ? = 5
[[1,2,4,5],[3],[6]]
 => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
 => ? = 5
Description
The order of promotion on a Gelfand-Tsetlin pattern.