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Your data matches 50 different statistics following compositions of up to 3 maps.
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Matching statistic: St000260
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1],[2]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 1
[[1],[3]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 1
[[2],[3]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 1
[[1],[4]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 1
[[2],[4]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 1
[[3],[4]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 1
[[1],[2],[3]]
=> [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 1
[[1,1],[2,2]]
=> [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 2
[[1],[5]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 1
[[2],[5]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 1
[[3],[5]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 1
[[4],[5]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 1
[[1],[2],[4]]
=> [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 1
[[1],[3],[4]]
=> [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 1
[[2],[3],[4]]
=> [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 1
[[1,1],[2,3]]
=> [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 2
[[1,1],[3,3]]
=> [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 2
[[1,2],[2,3]]
=> [2,4,1,3] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[[1,2],[3,3]]
=> [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 2
[[2,2],[3,3]]
=> [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 2
[[1],[6]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 1
[[2],[6]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 1
[[3],[6]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 1
[[4],[6]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 1
[[5],[6]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 1
[[1],[2],[5]]
=> [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 1
[[1],[3],[5]]
=> [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 1
[[1],[4],[5]]
=> [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 1
[[2],[3],[5]]
=> [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 1
[[2],[4],[5]]
=> [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 1
[[3],[4],[5]]
=> [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 1
[[1,1],[2,4]]
=> [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 2
[[1,1],[3,4]]
=> [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 2
[[1,1],[4,4]]
=> [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 2
[[1,2],[2,4]]
=> [2,4,1,3] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[[1,2],[3,4]]
=> [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 2
[[1,3],[2,4]]
=> [2,4,1,3] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[[1,2],[4,4]]
=> [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 2
[[1,3],[3,4]]
=> [2,4,1,3] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[[1,3],[4,4]]
=> [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 2
[[2,2],[3,4]]
=> [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 2
[[2,2],[4,4]]
=> [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 2
[[2,3],[3,4]]
=> [2,4,1,3] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[[2,3],[4,4]]
=> [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 2
[[3,3],[4,4]]
=> [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 2
[[1],[2],[3],[4]]
=> [4,3,2,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[[1,1],[2,2],[3]]
=> [5,3,4,1,2] => [3,1,5,4,2] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 2
[[1,1],[2,3],[3]]
=> [4,3,5,1,2] => [4,3,1,5,2] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> 2
[[1,2],[2,3],[3]]
=> [4,2,5,1,3] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 2
[[1,1,1],[2,2,2]]
=> [4,5,6,1,2,3] => [4,1,5,2,6,3] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> 2
Description
The radius of a connected graph.
This is the minimum eccentricity of any vertex.
Matching statistic: St001960
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00325: Permutations —ones to leading⟶ Permutations
St001960: Permutations ⟶ ℤResult quality: 50% ●values known / values provided: 68%●distinct values known / distinct values provided: 50%
Mp00069: Permutations —complement⟶ Permutations
Mp00325: Permutations —ones to leading⟶ Permutations
St001960: Permutations ⟶ ℤResult quality: 50% ●values known / values provided: 68%●distinct values known / distinct values provided: 50%
Values
[[1],[2]]
=> [2,1] => [1,2] => [1,2] => 0 = 1 - 1
[[1],[3]]
=> [2,1] => [1,2] => [1,2] => 0 = 1 - 1
[[2],[3]]
=> [2,1] => [1,2] => [1,2] => 0 = 1 - 1
[[1],[4]]
=> [2,1] => [1,2] => [1,2] => 0 = 1 - 1
[[2],[4]]
=> [2,1] => [1,2] => [1,2] => 0 = 1 - 1
[[3],[4]]
=> [2,1] => [1,2] => [1,2] => 0 = 1 - 1
[[1],[2],[3]]
=> [3,2,1] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[[1,1],[2,2]]
=> [3,4,1,2] => [2,1,4,3] => [2,4,3,1] => 1 = 2 - 1
[[1],[5]]
=> [2,1] => [1,2] => [1,2] => 0 = 1 - 1
[[2],[5]]
=> [2,1] => [1,2] => [1,2] => 0 = 1 - 1
[[3],[5]]
=> [2,1] => [1,2] => [1,2] => 0 = 1 - 1
[[4],[5]]
=> [2,1] => [1,2] => [1,2] => 0 = 1 - 1
[[1],[2],[4]]
=> [3,2,1] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[[1],[3],[4]]
=> [3,2,1] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[[2],[3],[4]]
=> [3,2,1] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[[1,1],[2,3]]
=> [3,4,1,2] => [2,1,4,3] => [2,4,3,1] => 1 = 2 - 1
[[1,1],[3,3]]
=> [3,4,1,2] => [2,1,4,3] => [2,4,3,1] => 1 = 2 - 1
[[1,2],[2,3]]
=> [2,4,1,3] => [3,1,4,2] => [2,4,1,3] => 0 = 1 - 1
[[1,2],[3,3]]
=> [3,4,1,2] => [2,1,4,3] => [2,4,3,1] => 1 = 2 - 1
[[2,2],[3,3]]
=> [3,4,1,2] => [2,1,4,3] => [2,4,3,1] => 1 = 2 - 1
[[1],[6]]
=> [2,1] => [1,2] => [1,2] => 0 = 1 - 1
[[2],[6]]
=> [2,1] => [1,2] => [1,2] => 0 = 1 - 1
[[3],[6]]
=> [2,1] => [1,2] => [1,2] => 0 = 1 - 1
[[4],[6]]
=> [2,1] => [1,2] => [1,2] => 0 = 1 - 1
[[5],[6]]
=> [2,1] => [1,2] => [1,2] => 0 = 1 - 1
[[1],[2],[5]]
=> [3,2,1] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[[1],[3],[5]]
=> [3,2,1] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[[1],[4],[5]]
=> [3,2,1] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[[2],[3],[5]]
=> [3,2,1] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[[2],[4],[5]]
=> [3,2,1] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[[3],[4],[5]]
=> [3,2,1] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[[1,1],[2,4]]
=> [3,4,1,2] => [2,1,4,3] => [2,4,3,1] => 1 = 2 - 1
[[1,1],[3,4]]
=> [3,4,1,2] => [2,1,4,3] => [2,4,3,1] => 1 = 2 - 1
[[1,1],[4,4]]
=> [3,4,1,2] => [2,1,4,3] => [2,4,3,1] => 1 = 2 - 1
[[1,2],[2,4]]
=> [2,4,1,3] => [3,1,4,2] => [2,4,1,3] => 0 = 1 - 1
[[1,2],[3,4]]
=> [3,4,1,2] => [2,1,4,3] => [2,4,3,1] => 1 = 2 - 1
[[1,3],[2,4]]
=> [2,4,1,3] => [3,1,4,2] => [2,4,1,3] => 0 = 1 - 1
[[1,2],[4,4]]
=> [3,4,1,2] => [2,1,4,3] => [2,4,3,1] => 1 = 2 - 1
[[1,3],[3,4]]
=> [2,4,1,3] => [3,1,4,2] => [2,4,1,3] => 0 = 1 - 1
[[1,3],[4,4]]
=> [3,4,1,2] => [2,1,4,3] => [2,4,3,1] => 1 = 2 - 1
[[2,2],[3,4]]
=> [3,4,1,2] => [2,1,4,3] => [2,4,3,1] => 1 = 2 - 1
[[2,2],[4,4]]
=> [3,4,1,2] => [2,1,4,3] => [2,4,3,1] => 1 = 2 - 1
[[2,3],[3,4]]
=> [2,4,1,3] => [3,1,4,2] => [2,4,1,3] => 0 = 1 - 1
[[2,3],[4,4]]
=> [3,4,1,2] => [2,1,4,3] => [2,4,3,1] => 1 = 2 - 1
[[3,3],[4,4]]
=> [3,4,1,2] => [2,1,4,3] => [2,4,3,1] => 1 = 2 - 1
[[1],[2],[3],[4]]
=> [4,3,2,1] => [1,2,3,4] => [1,2,3,4] => 0 = 1 - 1
[[1,1],[2,2],[3]]
=> [5,3,4,1,2] => [1,3,2,5,4] => [2,3,5,4,1] => 1 = 2 - 1
[[1,1],[2,3],[3]]
=> [4,3,5,1,2] => [2,3,1,5,4] => [2,5,3,4,1] => 1 = 2 - 1
[[1,2],[2,3],[3]]
=> [4,2,5,1,3] => [2,4,1,5,3] => [2,5,3,1,4] => 1 = 2 - 1
[[1,1,1],[2,2,2]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[1],[7]]
=> [2,1] => [1,2] => [1,2] => 0 = 1 - 1
[[1,1,1],[2,2,3]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[1,1,1],[2,3,3]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[1,1,1],[3,3,3]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[1,1,2],[2,2,3]]
=> [3,4,6,1,2,5] => [4,3,1,6,5,2] => [3,6,2,1,4,5] => ? = 1 - 1
[[1,1,2],[2,3,3]]
=> [3,5,6,1,2,4] => [4,2,1,6,5,3] => [3,6,5,2,1,4] => ? = 2 - 1
[[1,1,2],[3,3,3]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[1,2,2],[2,3,3]]
=> [2,5,6,1,3,4] => [5,2,1,6,4,3] => [3,6,5,2,4,1] => ? = 2 - 1
[[1,2,2],[3,3,3]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[2,2,2],[3,3,3]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[1,1,2],[2,3],[3]]
=> [5,3,6,1,2,4] => [2,4,1,6,5,3] => [3,6,4,2,1,5] => ? = 3 - 1
[[1,2,2],[2,3],[3]]
=> [5,2,6,1,3,4] => [2,5,1,6,4,3] => [3,6,4,2,5,1] => ? = 2 - 1
[[1,1],[2,2],[3,3]]
=> [5,6,3,4,1,2] => [2,1,4,3,6,5] => [2,4,3,6,5,1] => ? = 2 - 1
[[1,1,1],[2,2,4]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[1,1,1],[2,3,4]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[1,1,1],[2,4,4]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[1,1,1],[3,3,4]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[1,1,1],[3,4,4]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[1,1,1],[4,4,4]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[1,1,2],[2,2,4]]
=> [3,4,6,1,2,5] => [4,3,1,6,5,2] => [3,6,2,1,4,5] => ? = 1 - 1
[[1,1,2],[2,3,4]]
=> [3,5,6,1,2,4] => [4,2,1,6,5,3] => [3,6,5,2,1,4] => ? = 2 - 1
[[1,1,3],[2,2,4]]
=> [3,4,6,1,2,5] => [4,3,1,6,5,2] => [3,6,2,1,4,5] => ? = 1 - 1
[[1,1,2],[2,4,4]]
=> [3,5,6,1,2,4] => [4,2,1,6,5,3] => [3,6,5,2,1,4] => ? = 2 - 1
[[1,1,2],[3,3,4]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[1,1,3],[2,3,4]]
=> [3,4,6,1,2,5] => [4,3,1,6,5,2] => [3,6,2,1,4,5] => ? = 1 - 1
[[1,1,2],[3,4,4]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[1,1,3],[2,4,4]]
=> [3,5,6,1,2,4] => [4,2,1,6,5,3] => [3,6,5,2,1,4] => ? = 2 - 1
[[1,1,2],[4,4,4]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[1,1,3],[3,3,4]]
=> [3,4,6,1,2,5] => [4,3,1,6,5,2] => [3,6,2,1,4,5] => ? = 1 - 1
[[1,1,3],[3,4,4]]
=> [3,5,6,1,2,4] => [4,2,1,6,5,3] => [3,6,5,2,1,4] => ? = 2 - 1
[[1,1,3],[4,4,4]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[1,2,2],[2,3,4]]
=> [2,5,6,1,3,4] => [5,2,1,6,4,3] => [3,6,5,2,4,1] => ? = 2 - 1
[[1,2,2],[2,4,4]]
=> [2,5,6,1,3,4] => [5,2,1,6,4,3] => [3,6,5,2,4,1] => ? = 2 - 1
[[1,2,2],[3,3,4]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[1,2,3],[2,3,4]]
=> [2,4,6,1,3,5] => [5,3,1,6,4,2] => [3,6,2,4,1,5] => ? = 1 - 1
[[1,2,2],[3,4,4]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[1,2,3],[2,4,4]]
=> [2,5,6,1,3,4] => [5,2,1,6,4,3] => [3,6,5,2,4,1] => ? = 2 - 1
[[1,2,2],[4,4,4]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[1,2,3],[3,3,4]]
=> [3,4,6,1,2,5] => [4,3,1,6,5,2] => [3,6,2,1,4,5] => ? = 1 - 1
[[1,2,3],[3,4,4]]
=> [3,5,6,1,2,4] => [4,2,1,6,5,3] => [3,6,5,2,1,4] => ? = 2 - 1
[[1,3,3],[2,4,4]]
=> [2,5,6,1,3,4] => [5,2,1,6,4,3] => [3,6,5,2,4,1] => ? = 2 - 1
[[1,2,3],[4,4,4]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[1,3,3],[3,4,4]]
=> [2,5,6,1,3,4] => [5,2,1,6,4,3] => [3,6,5,2,4,1] => ? = 2 - 1
[[1,3,3],[4,4,4]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[2,2,2],[3,3,4]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[2,2,2],[3,4,4]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[2,2,2],[4,4,4]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
[[2,2,3],[3,3,4]]
=> [3,4,6,1,2,5] => [4,3,1,6,5,2] => [3,6,2,1,4,5] => ? = 1 - 1
[[2,2,3],[3,4,4]]
=> [3,5,6,1,2,4] => [4,2,1,6,5,3] => [3,6,5,2,1,4] => ? = 2 - 1
[[2,2,3],[4,4,4]]
=> [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,6,5,4,2,1] => ? = 2 - 1
Description
The number of descents of a permutation minus one if its first entry is not one.
This statistic appears in [1, Theorem 2.3] in a gamma-positivity result, see also [2].
Matching statistic: St001935
Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00305: Permutations —parking function⟶ Parking functions
St001935: Parking functions ⟶ ℤResult quality: 50% ●values known / values provided: 50%●distinct values known / distinct values provided: 75%
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00305: Permutations —parking function⟶ Parking functions
St001935: Parking functions ⟶ ℤResult quality: 50% ●values known / values provided: 50%●distinct values known / distinct values provided: 75%
Values
[[1],[2]]
=> [2,1] => [1,2] => [1,2] => 1
[[1],[3]]
=> [2,1] => [1,2] => [1,2] => 1
[[2],[3]]
=> [2,1] => [1,2] => [1,2] => 1
[[1],[4]]
=> [2,1] => [1,2] => [1,2] => 1
[[2],[4]]
=> [2,1] => [1,2] => [1,2] => 1
[[3],[4]]
=> [2,1] => [1,2] => [1,2] => 1
[[1],[2],[3]]
=> [3,2,1] => [1,3,2] => [1,3,2] => 1
[[1,1],[2,2]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 2
[[1],[5]]
=> [2,1] => [1,2] => [1,2] => 1
[[2],[5]]
=> [2,1] => [1,2] => [1,2] => 1
[[3],[5]]
=> [2,1] => [1,2] => [1,2] => 1
[[4],[5]]
=> [2,1] => [1,2] => [1,2] => 1
[[1],[2],[4]]
=> [3,2,1] => [1,3,2] => [1,3,2] => 1
[[1],[3],[4]]
=> [3,2,1] => [1,3,2] => [1,3,2] => 1
[[2],[3],[4]]
=> [3,2,1] => [1,3,2] => [1,3,2] => 1
[[1,1],[2,3]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 2
[[1,1],[3,3]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 2
[[1,2],[2,3]]
=> [2,4,1,3] => [4,2,1,3] => [4,2,1,3] => 1
[[1,2],[3,3]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 2
[[2,2],[3,3]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 2
[[1],[6]]
=> [2,1] => [1,2] => [1,2] => 1
[[2],[6]]
=> [2,1] => [1,2] => [1,2] => 1
[[3],[6]]
=> [2,1] => [1,2] => [1,2] => 1
[[4],[6]]
=> [2,1] => [1,2] => [1,2] => 1
[[5],[6]]
=> [2,1] => [1,2] => [1,2] => 1
[[1],[2],[5]]
=> [3,2,1] => [1,3,2] => [1,3,2] => 1
[[1],[3],[5]]
=> [3,2,1] => [1,3,2] => [1,3,2] => 1
[[1],[4],[5]]
=> [3,2,1] => [1,3,2] => [1,3,2] => 1
[[2],[3],[5]]
=> [3,2,1] => [1,3,2] => [1,3,2] => 1
[[2],[4],[5]]
=> [3,2,1] => [1,3,2] => [1,3,2] => 1
[[3],[4],[5]]
=> [3,2,1] => [1,3,2] => [1,3,2] => 1
[[1,1],[2,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 2
[[1,1],[3,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 2
[[1,1],[4,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 2
[[1,2],[2,4]]
=> [2,4,1,3] => [4,2,1,3] => [4,2,1,3] => 1
[[1,2],[3,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 2
[[1,3],[2,4]]
=> [2,4,1,3] => [4,2,1,3] => [4,2,1,3] => 1
[[1,2],[4,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 2
[[1,3],[3,4]]
=> [2,4,1,3] => [4,2,1,3] => [4,2,1,3] => 1
[[1,3],[4,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 2
[[2,2],[3,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 2
[[2,2],[4,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 2
[[2,3],[3,4]]
=> [2,4,1,3] => [4,2,1,3] => [4,2,1,3] => 1
[[2,3],[4,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 2
[[3,3],[4,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 2
[[1],[2],[3],[4]]
=> [4,3,2,1] => [1,4,3,2] => [1,4,3,2] => 1
[[1,1],[2,2],[3]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,1],[2,3],[3]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2
[[1,2],[2,3],[3]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 2
[[1,1,1],[2,2,2]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,6,1,2,3,4] => ? = 2
[[1],[7]]
=> [2,1] => [1,2] => [1,2] => 1
[[2],[7]]
=> [2,1] => [1,2] => [1,2] => 1
[[3],[7]]
=> [2,1] => [1,2] => [1,2] => 1
[[4],[7]]
=> [2,1] => [1,2] => [1,2] => 1
[[1,1],[2,2],[4]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,1],[2,3],[4]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,1],[2,4],[3]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2
[[1,1],[2,4],[4]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2
[[1,1],[3,3],[4]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,1],[3,4],[4]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2
[[1,2],[2,3],[4]]
=> [5,2,4,1,3] => [5,3,1,4,2] => [5,3,1,4,2] => ? = 1
[[1,2],[2,4],[3]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 2
[[1,2],[2,4],[4]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 2
[[1,2],[3,3],[4]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,3],[2,4],[3]]
=> [3,2,5,1,4] => [5,3,2,1,4] => [5,3,2,1,4] => ? = 2
[[1,2],[3,4],[4]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2
[[1,3],[2,4],[4]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 2
[[1,3],[3,4],[4]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 2
[[2,2],[3,3],[4]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[2,2],[3,4],[4]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2
[[2,3],[3,4],[4]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 2
[[1,1,1],[2,2,3]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,6,1,2,3,4] => ? = 2
[[1,1,1],[2,3,3]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,6,1,2,3,4] => ? = 2
[[1,1,1],[3,3,3]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,6,1,2,3,4] => ? = 2
[[1,1,2],[2,2,3]]
=> [3,4,6,1,2,5] => [5,6,2,3,1,4] => [5,6,2,3,1,4] => ? = 1
[[1,1,2],[2,3,3]]
=> [3,5,6,1,2,4] => [5,6,2,1,3,4] => [5,6,2,1,3,4] => ? = 2
[[1,1,2],[3,3,3]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,6,1,2,3,4] => ? = 2
[[1,2,2],[2,3,3]]
=> [2,5,6,1,3,4] => [5,2,6,1,3,4] => [5,2,6,1,3,4] => ? = 2
[[1,2,2],[3,3,3]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,6,1,2,3,4] => ? = 2
[[2,2,2],[3,3,3]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,6,1,2,3,4] => ? = 2
[[1,1,2],[2,3],[3]]
=> [5,3,6,1,2,4] => [5,6,3,1,2,4] => [5,6,3,1,2,4] => ? = 3
[[1,2,2],[2,3],[3]]
=> [5,2,6,1,3,4] => [5,3,6,1,2,4] => [5,3,6,1,2,4] => ? = 2
[[1,1],[2,2],[3,3]]
=> [5,6,3,4,1,2] => [6,1,4,5,2,3] => [6,1,4,5,2,3] => ? = 2
[[1,1],[2,2],[5]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,1],[2,3],[5]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,1],[2,5],[3]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2
[[1,1],[2,4],[5]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,1],[2,5],[4]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2
[[1,1],[2,5],[5]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2
[[1,1],[3,3],[5]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,1],[3,4],[5]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,1],[3,5],[4]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2
[[1,1],[3,5],[5]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2
[[1,1],[4,4],[5]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,1],[4,5],[5]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2
[[1,2],[2,3],[5]]
=> [5,2,4,1,3] => [5,3,1,4,2] => [5,3,1,4,2] => ? = 1
[[1,2],[2,5],[3]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 2
[[1,2],[2,4],[5]]
=> [5,2,4,1,3] => [5,3,1,4,2] => [5,3,1,4,2] => ? = 1
[[1,2],[2,5],[4]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 2
[[1,2],[2,5],[5]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 2
Description
The number of ascents in a parking function.
This is the number of indices i such that pi>pi+1.
Matching statistic: St001773
Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001773: Signed permutations ⟶ ℤResult quality: 50% ●values known / values provided: 50%●distinct values known / distinct values provided: 75%
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001773: Signed permutations ⟶ ℤResult quality: 50% ●values known / values provided: 50%●distinct values known / distinct values provided: 75%
Values
[[1],[2]]
=> [2,1] => [1,2] => [1,2] => 2 = 1 + 1
[[1],[3]]
=> [2,1] => [1,2] => [1,2] => 2 = 1 + 1
[[2],[3]]
=> [2,1] => [1,2] => [1,2] => 2 = 1 + 1
[[1],[4]]
=> [2,1] => [1,2] => [1,2] => 2 = 1 + 1
[[2],[4]]
=> [2,1] => [1,2] => [1,2] => 2 = 1 + 1
[[3],[4]]
=> [2,1] => [1,2] => [1,2] => 2 = 1 + 1
[[1],[2],[3]]
=> [3,2,1] => [1,3,2] => [1,3,2] => 2 = 1 + 1
[[1,1],[2,2]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 3 = 2 + 1
[[1],[5]]
=> [2,1] => [1,2] => [1,2] => 2 = 1 + 1
[[2],[5]]
=> [2,1] => [1,2] => [1,2] => 2 = 1 + 1
[[3],[5]]
=> [2,1] => [1,2] => [1,2] => 2 = 1 + 1
[[4],[5]]
=> [2,1] => [1,2] => [1,2] => 2 = 1 + 1
[[1],[2],[4]]
=> [3,2,1] => [1,3,2] => [1,3,2] => 2 = 1 + 1
[[1],[3],[4]]
=> [3,2,1] => [1,3,2] => [1,3,2] => 2 = 1 + 1
[[2],[3],[4]]
=> [3,2,1] => [1,3,2] => [1,3,2] => 2 = 1 + 1
[[1,1],[2,3]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 3 = 2 + 1
[[1,1],[3,3]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 3 = 2 + 1
[[1,2],[2,3]]
=> [2,4,1,3] => [4,2,1,3] => [4,2,1,3] => 2 = 1 + 1
[[1,2],[3,3]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 3 = 2 + 1
[[2,2],[3,3]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 3 = 2 + 1
[[1],[6]]
=> [2,1] => [1,2] => [1,2] => 2 = 1 + 1
[[2],[6]]
=> [2,1] => [1,2] => [1,2] => 2 = 1 + 1
[[3],[6]]
=> [2,1] => [1,2] => [1,2] => 2 = 1 + 1
[[4],[6]]
=> [2,1] => [1,2] => [1,2] => 2 = 1 + 1
[[5],[6]]
=> [2,1] => [1,2] => [1,2] => 2 = 1 + 1
[[1],[2],[5]]
=> [3,2,1] => [1,3,2] => [1,3,2] => 2 = 1 + 1
[[1],[3],[5]]
=> [3,2,1] => [1,3,2] => [1,3,2] => 2 = 1 + 1
[[1],[4],[5]]
=> [3,2,1] => [1,3,2] => [1,3,2] => 2 = 1 + 1
[[2],[3],[5]]
=> [3,2,1] => [1,3,2] => [1,3,2] => 2 = 1 + 1
[[2],[4],[5]]
=> [3,2,1] => [1,3,2] => [1,3,2] => 2 = 1 + 1
[[3],[4],[5]]
=> [3,2,1] => [1,3,2] => [1,3,2] => 2 = 1 + 1
[[1,1],[2,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 3 = 2 + 1
[[1,1],[3,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 3 = 2 + 1
[[1,1],[4,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 3 = 2 + 1
[[1,2],[2,4]]
=> [2,4,1,3] => [4,2,1,3] => [4,2,1,3] => 2 = 1 + 1
[[1,2],[3,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 3 = 2 + 1
[[1,3],[2,4]]
=> [2,4,1,3] => [4,2,1,3] => [4,2,1,3] => 2 = 1 + 1
[[1,2],[4,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 3 = 2 + 1
[[1,3],[3,4]]
=> [2,4,1,3] => [4,2,1,3] => [4,2,1,3] => 2 = 1 + 1
[[1,3],[4,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 3 = 2 + 1
[[2,2],[3,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 3 = 2 + 1
[[2,2],[4,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 3 = 2 + 1
[[2,3],[3,4]]
=> [2,4,1,3] => [4,2,1,3] => [4,2,1,3] => 2 = 1 + 1
[[2,3],[4,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 3 = 2 + 1
[[3,3],[4,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 3 = 2 + 1
[[1],[2],[3],[4]]
=> [4,3,2,1] => [1,4,3,2] => [1,4,3,2] => 2 = 1 + 1
[[1,1],[2,2],[3]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2 + 1
[[1,1],[2,3],[3]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2 + 1
[[1,2],[2,3],[3]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 2 + 1
[[1,1,1],[2,2,2]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,6,1,2,3,4] => ? = 2 + 1
[[1],[7]]
=> [2,1] => [1,2] => [1,2] => 2 = 1 + 1
[[2],[7]]
=> [2,1] => [1,2] => [1,2] => 2 = 1 + 1
[[3],[7]]
=> [2,1] => [1,2] => [1,2] => 2 = 1 + 1
[[4],[7]]
=> [2,1] => [1,2] => [1,2] => 2 = 1 + 1
[[1,1],[2,2],[4]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2 + 1
[[1,1],[2,3],[4]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2 + 1
[[1,1],[2,4],[3]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2 + 1
[[1,1],[2,4],[4]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2 + 1
[[1,1],[3,3],[4]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2 + 1
[[1,1],[3,4],[4]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2 + 1
[[1,2],[2,3],[4]]
=> [5,2,4,1,3] => [5,3,1,4,2] => [5,3,1,4,2] => ? = 1 + 1
[[1,2],[2,4],[3]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 2 + 1
[[1,2],[2,4],[4]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 2 + 1
[[1,2],[3,3],[4]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2 + 1
[[1,3],[2,4],[3]]
=> [3,2,5,1,4] => [5,3,2,1,4] => [5,3,2,1,4] => ? = 2 + 1
[[1,2],[3,4],[4]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2 + 1
[[1,3],[2,4],[4]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 2 + 1
[[1,3],[3,4],[4]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 2 + 1
[[2,2],[3,3],[4]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2 + 1
[[2,2],[3,4],[4]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2 + 1
[[2,3],[3,4],[4]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 2 + 1
[[1,1,1],[2,2,3]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,6,1,2,3,4] => ? = 2 + 1
[[1,1,1],[2,3,3]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,6,1,2,3,4] => ? = 2 + 1
[[1,1,1],[3,3,3]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,6,1,2,3,4] => ? = 2 + 1
[[1,1,2],[2,2,3]]
=> [3,4,6,1,2,5] => [5,6,2,3,1,4] => [5,6,2,3,1,4] => ? = 1 + 1
[[1,1,2],[2,3,3]]
=> [3,5,6,1,2,4] => [5,6,2,1,3,4] => [5,6,2,1,3,4] => ? = 2 + 1
[[1,1,2],[3,3,3]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,6,1,2,3,4] => ? = 2 + 1
[[1,2,2],[2,3,3]]
=> [2,5,6,1,3,4] => [5,2,6,1,3,4] => [5,2,6,1,3,4] => ? = 2 + 1
[[1,2,2],[3,3,3]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,6,1,2,3,4] => ? = 2 + 1
[[2,2,2],[3,3,3]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,6,1,2,3,4] => ? = 2 + 1
[[1,1,2],[2,3],[3]]
=> [5,3,6,1,2,4] => [5,6,3,1,2,4] => [5,6,3,1,2,4] => ? = 3 + 1
[[1,2,2],[2,3],[3]]
=> [5,2,6,1,3,4] => [5,3,6,1,2,4] => [5,3,6,1,2,4] => ? = 2 + 1
[[1,1],[2,2],[3,3]]
=> [5,6,3,4,1,2] => [6,1,4,5,2,3] => [6,1,4,5,2,3] => ? = 2 + 1
[[1,1],[2,2],[5]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2 + 1
[[1,1],[2,3],[5]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2 + 1
[[1,1],[2,5],[3]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2 + 1
[[1,1],[2,4],[5]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2 + 1
[[1,1],[2,5],[4]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2 + 1
[[1,1],[2,5],[5]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2 + 1
[[1,1],[3,3],[5]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2 + 1
[[1,1],[3,4],[5]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2 + 1
[[1,1],[3,5],[4]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2 + 1
[[1,1],[3,5],[5]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2 + 1
[[1,1],[4,4],[5]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2 + 1
[[1,1],[4,5],[5]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2 + 1
[[1,2],[2,3],[5]]
=> [5,2,4,1,3] => [5,3,1,4,2] => [5,3,1,4,2] => ? = 1 + 1
[[1,2],[2,5],[3]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 2 + 1
[[1,2],[2,4],[5]]
=> [5,2,4,1,3] => [5,3,1,4,2] => [5,3,1,4,2] => ? = 1 + 1
[[1,2],[2,5],[4]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 2 + 1
[[1,2],[2,5],[5]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 2 + 1
Description
The number of minimal elements in Bruhat order not less than the signed permutation.
The minimal elements in question are biGrassmannian, that is both the element and its inverse have at most one descent.
This is the size of the essential set of the signed permutation, see [1].
Matching statistic: St001095
Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001095: Posets ⟶ ℤResult quality: 49% ●values known / values provided: 49%●distinct values known / distinct values provided: 50%
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001095: Posets ⟶ ℤResult quality: 49% ●values known / values provided: 49%●distinct values known / distinct values provided: 50%
Values
[[1],[2]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 0 = 1 - 1
[[1],[3]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 0 = 1 - 1
[[2],[3]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 0 = 1 - 1
[[1],[4]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 0 = 1 - 1
[[2],[4]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 0 = 1 - 1
[[3],[4]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 0 = 1 - 1
[[1],[2],[3]]
=> [3,2,1] => [3,2,1] => ([(0,2),(2,1)],3)
=> 0 = 1 - 1
[[1,1],[2,2]]
=> [3,4,1,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 2 - 1
[[1],[5]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 0 = 1 - 1
[[2],[5]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 0 = 1 - 1
[[3],[5]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 0 = 1 - 1
[[4],[5]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 0 = 1 - 1
[[1],[2],[4]]
=> [3,2,1] => [3,2,1] => ([(0,2),(2,1)],3)
=> 0 = 1 - 1
[[1],[3],[4]]
=> [3,2,1] => [3,2,1] => ([(0,2),(2,1)],3)
=> 0 = 1 - 1
[[2],[3],[4]]
=> [3,2,1] => [3,2,1] => ([(0,2),(2,1)],3)
=> 0 = 1 - 1
[[1,1],[2,3]]
=> [3,4,1,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 2 - 1
[[1,1],[3,3]]
=> [3,4,1,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 2 - 1
[[1,2],[2,3]]
=> [2,4,1,3] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 0 = 1 - 1
[[1,2],[3,3]]
=> [3,4,1,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 2 - 1
[[2,2],[3,3]]
=> [3,4,1,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 2 - 1
[[1],[6]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 0 = 1 - 1
[[2],[6]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 0 = 1 - 1
[[3],[6]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 0 = 1 - 1
[[4],[6]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 0 = 1 - 1
[[5],[6]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 0 = 1 - 1
[[1],[2],[5]]
=> [3,2,1] => [3,2,1] => ([(0,2),(2,1)],3)
=> 0 = 1 - 1
[[1],[3],[5]]
=> [3,2,1] => [3,2,1] => ([(0,2),(2,1)],3)
=> 0 = 1 - 1
[[1],[4],[5]]
=> [3,2,1] => [3,2,1] => ([(0,2),(2,1)],3)
=> 0 = 1 - 1
[[2],[3],[5]]
=> [3,2,1] => [3,2,1] => ([(0,2),(2,1)],3)
=> 0 = 1 - 1
[[2],[4],[5]]
=> [3,2,1] => [3,2,1] => ([(0,2),(2,1)],3)
=> 0 = 1 - 1
[[3],[4],[5]]
=> [3,2,1] => [3,2,1] => ([(0,2),(2,1)],3)
=> 0 = 1 - 1
[[1,1],[2,4]]
=> [3,4,1,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 2 - 1
[[1,1],[3,4]]
=> [3,4,1,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 2 - 1
[[1,1],[4,4]]
=> [3,4,1,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 2 - 1
[[1,2],[2,4]]
=> [2,4,1,3] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 0 = 1 - 1
[[1,2],[3,4]]
=> [3,4,1,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 2 - 1
[[1,3],[2,4]]
=> [2,4,1,3] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 0 = 1 - 1
[[1,2],[4,4]]
=> [3,4,1,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 2 - 1
[[1,3],[3,4]]
=> [2,4,1,3] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 0 = 1 - 1
[[1,3],[4,4]]
=> [3,4,1,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 2 - 1
[[2,2],[3,4]]
=> [3,4,1,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 2 - 1
[[2,2],[4,4]]
=> [3,4,1,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 2 - 1
[[2,3],[3,4]]
=> [2,4,1,3] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 0 = 1 - 1
[[2,3],[4,4]]
=> [3,4,1,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 2 - 1
[[3,3],[4,4]]
=> [3,4,1,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> 1 = 2 - 1
[[1],[2],[3],[4]]
=> [4,3,2,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 0 = 1 - 1
[[1,1],[2,2],[3]]
=> [5,3,4,1,2] => [1,3,5,4,2] => ([(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
[[1,1],[2,3],[3]]
=> [4,3,5,1,2] => [1,4,3,5,2] => ([(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],[2,3],[3]]
=> [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
[[1,1,1],[2,2,2]]
=> [4,5,6,1,2,3] => [1,2,4,5,6,3] => ([(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)
=> ? = 2 - 1
[[1],[7]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 0 = 1 - 1
[[2],[7]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 0 = 1 - 1
[[3],[7]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 0 = 1 - 1
[[4],[7]]
=> [2,1] => [2,1] => ([(0,1)],2)
=> 0 = 1 - 1
[[1,1],[2,2],[4]]
=> [5,3,4,1,2] => [1,3,5,4,2] => ([(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
[[1,1],[2,3],[4]]
=> [5,3,4,1,2] => [1,3,5,4,2] => ([(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
[[1,1],[2,4],[3]]
=> [4,3,5,1,2] => [1,4,3,5,2] => ([(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
[[1,1],[2,4],[4]]
=> [4,3,5,1,2] => [1,4,3,5,2] => ([(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
[[1,1],[3,3],[4]]
=> [5,3,4,1,2] => [1,3,5,4,2] => ([(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
[[1,1],[3,4],[4]]
=> [4,3,5,1,2] => [1,4,3,5,2] => ([(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],[2,3],[4]]
=> [5,2,4,1,3] => [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)
=> ? = 1 - 1
[[1,2],[2,4],[3]]
=> [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],[2,4],[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],[3,3],[4]]
=> [5,3,4,1,2] => [1,3,5,4,2] => ([(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
[[1,3],[2,4],[3]]
=> [3,2,5,1,4] => [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)
=> ? = 2 - 1
[[1,2],[3,4],[4]]
=> [4,3,5,1,2] => [1,4,3,5,2] => ([(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
[[1,3],[2,4],[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
[[1,3],[3,4],[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
[[2,2],[3,3],[4]]
=> [5,3,4,1,2] => [1,3,5,4,2] => ([(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
[[2,2],[3,4],[4]]
=> [4,3,5,1,2] => [1,4,3,5,2] => ([(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
[[2,3],[3,4],[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
[[1,1,1],[2,2,3]]
=> [4,5,6,1,2,3] => [1,2,4,5,6,3] => ([(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)
=> ? = 2 - 1
[[1,1,1],[2,3,3]]
=> [4,5,6,1,2,3] => [1,2,4,5,6,3] => ([(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)
=> ? = 2 - 1
[[1,1,1],[3,3,3]]
=> [4,5,6,1,2,3] => [1,2,4,5,6,3] => ([(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)
=> ? = 2 - 1
[[1,1,2],[2,2,3]]
=> [3,4,6,1,2,5] => [1,3,4,2,6,5] => ([(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)
=> ? = 1 - 1
[[1,1,2],[2,3,3]]
=> [3,5,6,1,2,4] => [1,3,2,5,6,4] => ([(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)
=> ? = 2 - 1
[[1,1,2],[3,3,3]]
=> [4,5,6,1,2,3] => [1,2,4,5,6,3] => ([(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)
=> ? = 2 - 1
[[1,2,2],[2,3,3]]
=> [2,5,6,1,3,4] => [2,1,3,5,6,4] => ([(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)
=> ? = 2 - 1
[[1,2,2],[3,3,3]]
=> [4,5,6,1,2,3] => [1,2,4,5,6,3] => ([(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)
=> ? = 2 - 1
[[2,2,2],[3,3,3]]
=> [4,5,6,1,2,3] => [1,2,4,5,6,3] => ([(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)
=> ? = 2 - 1
[[1,1,2],[2,3],[3]]
=> [5,3,6,1,2,4] => [1,3,5,2,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(1,16),(1,20),(2,8),(2,16),(2,17),(3,9),(3,10),(3,17),(3,20),(4,12),(4,13),(4,16),(4,17),(4,20),(5,11),(5,13),(5,16),(5,17),(5,20),(6,8),(6,10),(6,11),(6,12),(6,20),(8,19),(8,23),(9,22),(10,15),(10,19),(10,22),(11,14),(11,15),(11,19),(11,23),(12,14),(12,15),(12,19),(12,23),(13,14),(13,22),(13,23),(14,18),(14,21),(15,18),(15,21),(16,22),(16,23),(17,19),(17,22),(17,23),(18,7),(19,18),(19,21),(20,15),(20,22),(20,23),(21,7),(22,21),(23,18),(23,21)],24)
=> ? = 3 - 1
[[1,2,2],[2,3],[3]]
=> [5,2,6,1,3,4] => [2,1,5,3,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,6),(1,10),(1,15),(1,16),(2,11),(2,15),(2,16),(3,13),(3,15),(3,16),(4,12),(4,15),(4,16),(5,8),(5,9),(5,14),(5,20),(6,5),(6,10),(6,11),(6,12),(6,13),(8,17),(8,19),(9,17),(9,19),(10,18),(10,20),(11,14),(11,18),(11,20),(12,8),(12,18),(12,20),(13,9),(13,18),(13,20),(14,17),(14,19),(15,14),(15,20),(16,14),(16,18),(17,7),(18,19),(19,7),(20,17),(20,19)],21)
=> ? = 2 - 1
[[1,1],[2,2],[3,3]]
=> [5,6,3,4,1,2] => [1,3,5,6,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(1,19),(2,9),(2,12),(2,19),(3,8),(3,12),(3,19),(4,6),(4,8),(4,10),(4,19),(5,6),(5,9),(5,11),(5,19),(6,13),(6,17),(6,18),(8,16),(8,17),(9,16),(9,18),(10,13),(10,17),(11,13),(11,18),(12,16),(13,15),(14,7),(15,7),(16,14),(17,14),(17,15),(18,14),(18,15),(19,16),(19,17),(19,18)],20)
=> ? = 2 - 1
[[1,1],[2,2],[5]]
=> [5,3,4,1,2] => [1,3,5,4,2] => ([(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
[[1,1],[2,3],[5]]
=> [5,3,4,1,2] => [1,3,5,4,2] => ([(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
[[1,1],[2,5],[3]]
=> [4,3,5,1,2] => [1,4,3,5,2] => ([(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
[[1,1],[2,4],[5]]
=> [5,3,4,1,2] => [1,3,5,4,2] => ([(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
[[1,1],[2,5],[4]]
=> [4,3,5,1,2] => [1,4,3,5,2] => ([(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
[[1,1],[2,5],[5]]
=> [4,3,5,1,2] => [1,4,3,5,2] => ([(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
[[1,1],[3,3],[5]]
=> [5,3,4,1,2] => [1,3,5,4,2] => ([(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
[[1,1],[3,4],[5]]
=> [5,3,4,1,2] => [1,3,5,4,2] => ([(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
[[1,1],[3,5],[4]]
=> [4,3,5,1,2] => [1,4,3,5,2] => ([(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
[[1,1],[3,5],[5]]
=> [4,3,5,1,2] => [1,4,3,5,2] => ([(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
[[1,1],[4,4],[5]]
=> [5,3,4,1,2] => [1,3,5,4,2] => ([(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
[[1,1],[4,5],[5]]
=> [4,3,5,1,2] => [1,4,3,5,2] => ([(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],[2,3],[5]]
=> [5,2,4,1,3] => [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)
=> ? = 1 - 1
[[1,2],[2,5],[3]]
=> [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],[2,4],[5]]
=> [5,2,4,1,3] => [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)
=> ? = 1 - 1
[[1,2],[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],[2,5],[5]]
=> [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
Description
The number of non-isomorphic posets with precisely one further covering relation.
Matching statistic: St001860
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001860: Signed permutations ⟶ ℤResult quality: 48% ●values known / values provided: 48%●distinct values known / distinct values provided: 50%
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001860: Signed permutations ⟶ ℤResult quality: 48% ●values known / values provided: 48%●distinct values known / distinct values provided: 50%
Values
[[1],[2]]
=> [2,1] => [2,1] => 1
[[1],[3]]
=> [2,1] => [2,1] => 1
[[2],[3]]
=> [2,1] => [2,1] => 1
[[1],[4]]
=> [2,1] => [2,1] => 1
[[2],[4]]
=> [2,1] => [2,1] => 1
[[3],[4]]
=> [2,1] => [2,1] => 1
[[1],[2],[3]]
=> [3,2,1] => [3,2,1] => 1
[[1,1],[2,2]]
=> [3,4,1,2] => [3,4,1,2] => 2
[[1],[5]]
=> [2,1] => [2,1] => 1
[[2],[5]]
=> [2,1] => [2,1] => 1
[[3],[5]]
=> [2,1] => [2,1] => 1
[[4],[5]]
=> [2,1] => [2,1] => 1
[[1],[2],[4]]
=> [3,2,1] => [3,2,1] => 1
[[1],[3],[4]]
=> [3,2,1] => [3,2,1] => 1
[[2],[3],[4]]
=> [3,2,1] => [3,2,1] => 1
[[1,1],[2,3]]
=> [3,4,1,2] => [3,4,1,2] => 2
[[1,1],[3,3]]
=> [3,4,1,2] => [3,4,1,2] => 2
[[1,2],[2,3]]
=> [2,4,1,3] => [2,4,1,3] => 1
[[1,2],[3,3]]
=> [3,4,1,2] => [3,4,1,2] => 2
[[2,2],[3,3]]
=> [3,4,1,2] => [3,4,1,2] => 2
[[1],[6]]
=> [2,1] => [2,1] => 1
[[2],[6]]
=> [2,1] => [2,1] => 1
[[3],[6]]
=> [2,1] => [2,1] => 1
[[4],[6]]
=> [2,1] => [2,1] => 1
[[5],[6]]
=> [2,1] => [2,1] => 1
[[1],[2],[5]]
=> [3,2,1] => [3,2,1] => 1
[[1],[3],[5]]
=> [3,2,1] => [3,2,1] => 1
[[1],[4],[5]]
=> [3,2,1] => [3,2,1] => 1
[[2],[3],[5]]
=> [3,2,1] => [3,2,1] => 1
[[2],[4],[5]]
=> [3,2,1] => [3,2,1] => 1
[[3],[4],[5]]
=> [3,2,1] => [3,2,1] => 1
[[1,1],[2,4]]
=> [3,4,1,2] => [3,4,1,2] => 2
[[1,1],[3,4]]
=> [3,4,1,2] => [3,4,1,2] => 2
[[1,1],[4,4]]
=> [3,4,1,2] => [3,4,1,2] => 2
[[1,2],[2,4]]
=> [2,4,1,3] => [2,4,1,3] => 1
[[1,2],[3,4]]
=> [3,4,1,2] => [3,4,1,2] => 2
[[1,3],[2,4]]
=> [2,4,1,3] => [2,4,1,3] => 1
[[1,2],[4,4]]
=> [3,4,1,2] => [3,4,1,2] => 2
[[1,3],[3,4]]
=> [2,4,1,3] => [2,4,1,3] => 1
[[1,3],[4,4]]
=> [3,4,1,2] => [3,4,1,2] => 2
[[2,2],[3,4]]
=> [3,4,1,2] => [3,4,1,2] => 2
[[2,2],[4,4]]
=> [3,4,1,2] => [3,4,1,2] => 2
[[2,3],[3,4]]
=> [2,4,1,3] => [2,4,1,3] => 1
[[2,3],[4,4]]
=> [3,4,1,2] => [3,4,1,2] => 2
[[3,3],[4,4]]
=> [3,4,1,2] => [3,4,1,2] => 2
[[1],[2],[3],[4]]
=> [4,3,2,1] => [4,3,2,1] => 1
[[1,1],[2,2],[3]]
=> [5,3,4,1,2] => [5,3,4,1,2] => ? = 2
[[1,1],[2,3],[3]]
=> [4,3,5,1,2] => [4,3,5,1,2] => ? = 2
[[1,2],[2,3],[3]]
=> [4,2,5,1,3] => [4,2,5,1,3] => ? = 2
[[1,1,1],[2,2,2]]
=> [4,5,6,1,2,3] => [4,5,6,1,2,3] => ? = 2
[[1],[7]]
=> [2,1] => [2,1] => 1
[[2],[7]]
=> [2,1] => [2,1] => 1
[[3],[7]]
=> [2,1] => [2,1] => 1
[[4],[7]]
=> [2,1] => [2,1] => 1
[[1,1],[2,2],[4]]
=> [5,3,4,1,2] => [5,3,4,1,2] => ? = 2
[[1,1],[2,3],[4]]
=> [5,3,4,1,2] => [5,3,4,1,2] => ? = 2
[[1,1],[2,4],[3]]
=> [4,3,5,1,2] => [4,3,5,1,2] => ? = 2
[[1,1],[2,4],[4]]
=> [4,3,5,1,2] => [4,3,5,1,2] => ? = 2
[[1,1],[3,3],[4]]
=> [5,3,4,1,2] => [5,3,4,1,2] => ? = 2
[[1,1],[3,4],[4]]
=> [4,3,5,1,2] => [4,3,5,1,2] => ? = 2
[[1,2],[2,3],[4]]
=> [5,2,4,1,3] => [5,2,4,1,3] => ? = 1
[[1,2],[2,4],[3]]
=> [4,2,5,1,3] => [4,2,5,1,3] => ? = 2
[[1,2],[2,4],[4]]
=> [4,2,5,1,3] => [4,2,5,1,3] => ? = 2
[[1,2],[3,3],[4]]
=> [5,3,4,1,2] => [5,3,4,1,2] => ? = 2
[[1,3],[2,4],[3]]
=> [3,2,5,1,4] => [3,2,5,1,4] => ? = 2
[[1,2],[3,4],[4]]
=> [4,3,5,1,2] => [4,3,5,1,2] => ? = 2
[[1,3],[2,4],[4]]
=> [4,2,5,1,3] => [4,2,5,1,3] => ? = 2
[[1,3],[3,4],[4]]
=> [4,2,5,1,3] => [4,2,5,1,3] => ? = 2
[[2,2],[3,3],[4]]
=> [5,3,4,1,2] => [5,3,4,1,2] => ? = 2
[[2,2],[3,4],[4]]
=> [4,3,5,1,2] => [4,3,5,1,2] => ? = 2
[[2,3],[3,4],[4]]
=> [4,2,5,1,3] => [4,2,5,1,3] => ? = 2
[[1,1,1],[2,2,3]]
=> [4,5,6,1,2,3] => [4,5,6,1,2,3] => ? = 2
[[1,1,1],[2,3,3]]
=> [4,5,6,1,2,3] => [4,5,6,1,2,3] => ? = 2
[[1,1,1],[3,3,3]]
=> [4,5,6,1,2,3] => [4,5,6,1,2,3] => ? = 2
[[1,1,2],[2,2,3]]
=> [3,4,6,1,2,5] => [3,4,6,1,2,5] => ? = 1
[[1,1,2],[2,3,3]]
=> [3,5,6,1,2,4] => [3,5,6,1,2,4] => ? = 2
[[1,1,2],[3,3,3]]
=> [4,5,6,1,2,3] => [4,5,6,1,2,3] => ? = 2
[[1,2,2],[2,3,3]]
=> [2,5,6,1,3,4] => [2,5,6,1,3,4] => ? = 2
[[1,2,2],[3,3,3]]
=> [4,5,6,1,2,3] => [4,5,6,1,2,3] => ? = 2
[[2,2,2],[3,3,3]]
=> [4,5,6,1,2,3] => [4,5,6,1,2,3] => ? = 2
[[1,1,2],[2,3],[3]]
=> [5,3,6,1,2,4] => [5,3,6,1,2,4] => ? = 3
[[1,2,2],[2,3],[3]]
=> [5,2,6,1,3,4] => [5,2,6,1,3,4] => ? = 2
[[1,1],[2,2],[3,3]]
=> [5,6,3,4,1,2] => [5,6,3,4,1,2] => ? = 2
[[1,1],[2,2],[5]]
=> [5,3,4,1,2] => [5,3,4,1,2] => ? = 2
[[1,1],[2,3],[5]]
=> [5,3,4,1,2] => [5,3,4,1,2] => ? = 2
[[1,1],[2,5],[3]]
=> [4,3,5,1,2] => [4,3,5,1,2] => ? = 2
[[1,1],[2,4],[5]]
=> [5,3,4,1,2] => [5,3,4,1,2] => ? = 2
[[1,1],[2,5],[4]]
=> [4,3,5,1,2] => [4,3,5,1,2] => ? = 2
[[1,1],[2,5],[5]]
=> [4,3,5,1,2] => [4,3,5,1,2] => ? = 2
[[1,1],[3,3],[5]]
=> [5,3,4,1,2] => [5,3,4,1,2] => ? = 2
[[1,1],[3,4],[5]]
=> [5,3,4,1,2] => [5,3,4,1,2] => ? = 2
[[1,1],[3,5],[4]]
=> [4,3,5,1,2] => [4,3,5,1,2] => ? = 2
[[1,1],[3,5],[5]]
=> [4,3,5,1,2] => [4,3,5,1,2] => ? = 2
[[1,1],[4,4],[5]]
=> [5,3,4,1,2] => [5,3,4,1,2] => ? = 2
[[1,1],[4,5],[5]]
=> [4,3,5,1,2] => [4,3,5,1,2] => ? = 2
[[1,2],[2,3],[5]]
=> [5,2,4,1,3] => [5,2,4,1,3] => ? = 1
[[1,2],[2,5],[3]]
=> [4,2,5,1,3] => [4,2,5,1,3] => ? = 2
[[1,2],[2,4],[5]]
=> [5,2,4,1,3] => [5,2,4,1,3] => ? = 1
[[1,2],[2,5],[4]]
=> [4,2,5,1,3] => [4,2,5,1,3] => ? = 2
[[1,2],[2,5],[5]]
=> [4,2,5,1,3] => [4,2,5,1,3] => ? = 2
Description
The number of factors of the Stanley symmetric function associated with a signed permutation.
Matching statistic: St001582
(load all 6 compositions to match this statistic)
(load all 6 compositions to match this statistic)
Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00309: Permutations —inverse toric promotion⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
St001582: Permutations ⟶ ℤResult quality: 48% ●values known / values provided: 48%●distinct values known / distinct values provided: 50%
Mp00309: Permutations —inverse toric promotion⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
St001582: Permutations ⟶ ℤResult quality: 48% ●values known / values provided: 48%●distinct values known / distinct values provided: 50%
Values
[[1],[2]]
=> [2,1] => [2,1] => [1,2] => 1
[[1],[3]]
=> [2,1] => [2,1] => [1,2] => 1
[[2],[3]]
=> [2,1] => [2,1] => [1,2] => 1
[[1],[4]]
=> [2,1] => [2,1] => [1,2] => 1
[[2],[4]]
=> [2,1] => [2,1] => [1,2] => 1
[[3],[4]]
=> [2,1] => [2,1] => [1,2] => 1
[[1],[2],[3]]
=> [3,2,1] => [1,2,3] => [2,3,1] => 1
[[1,1],[2,2]]
=> [3,4,1,2] => [1,4,2,3] => [2,4,1,3] => 2
[[1],[5]]
=> [2,1] => [2,1] => [1,2] => 1
[[2],[5]]
=> [2,1] => [2,1] => [1,2] => 1
[[3],[5]]
=> [2,1] => [2,1] => [1,2] => 1
[[4],[5]]
=> [2,1] => [2,1] => [1,2] => 1
[[1],[2],[4]]
=> [3,2,1] => [1,2,3] => [2,3,1] => 1
[[1],[3],[4]]
=> [3,2,1] => [1,2,3] => [2,3,1] => 1
[[2],[3],[4]]
=> [3,2,1] => [1,2,3] => [2,3,1] => 1
[[1,1],[2,3]]
=> [3,4,1,2] => [1,4,2,3] => [2,4,1,3] => 2
[[1,1],[3,3]]
=> [3,4,1,2] => [1,4,2,3] => [2,4,1,3] => 2
[[1,2],[2,3]]
=> [2,4,1,3] => [1,3,2,4] => [2,4,3,1] => 1
[[1,2],[3,3]]
=> [3,4,1,2] => [1,4,2,3] => [2,4,1,3] => 2
[[2,2],[3,3]]
=> [3,4,1,2] => [1,4,2,3] => [2,4,1,3] => 2
[[1],[6]]
=> [2,1] => [2,1] => [1,2] => 1
[[2],[6]]
=> [2,1] => [2,1] => [1,2] => 1
[[3],[6]]
=> [2,1] => [2,1] => [1,2] => 1
[[4],[6]]
=> [2,1] => [2,1] => [1,2] => 1
[[5],[6]]
=> [2,1] => [2,1] => [1,2] => 1
[[1],[2],[5]]
=> [3,2,1] => [1,2,3] => [2,3,1] => 1
[[1],[3],[5]]
=> [3,2,1] => [1,2,3] => [2,3,1] => 1
[[1],[4],[5]]
=> [3,2,1] => [1,2,3] => [2,3,1] => 1
[[2],[3],[5]]
=> [3,2,1] => [1,2,3] => [2,3,1] => 1
[[2],[4],[5]]
=> [3,2,1] => [1,2,3] => [2,3,1] => 1
[[3],[4],[5]]
=> [3,2,1] => [1,2,3] => [2,3,1] => 1
[[1,1],[2,4]]
=> [3,4,1,2] => [1,4,2,3] => [2,4,1,3] => 2
[[1,1],[3,4]]
=> [3,4,1,2] => [1,4,2,3] => [2,4,1,3] => 2
[[1,1],[4,4]]
=> [3,4,1,2] => [1,4,2,3] => [2,4,1,3] => 2
[[1,2],[2,4]]
=> [2,4,1,3] => [1,3,2,4] => [2,4,3,1] => 1
[[1,2],[3,4]]
=> [3,4,1,2] => [1,4,2,3] => [2,4,1,3] => 2
[[1,3],[2,4]]
=> [2,4,1,3] => [1,3,2,4] => [2,4,3,1] => 1
[[1,2],[4,4]]
=> [3,4,1,2] => [1,4,2,3] => [2,4,1,3] => 2
[[1,3],[3,4]]
=> [2,4,1,3] => [1,3,2,4] => [2,4,3,1] => 1
[[1,3],[4,4]]
=> [3,4,1,2] => [1,4,2,3] => [2,4,1,3] => 2
[[2,2],[3,4]]
=> [3,4,1,2] => [1,4,2,3] => [2,4,1,3] => 2
[[2,2],[4,4]]
=> [3,4,1,2] => [1,4,2,3] => [2,4,1,3] => 2
[[2,3],[3,4]]
=> [2,4,1,3] => [1,3,2,4] => [2,4,3,1] => 1
[[2,3],[4,4]]
=> [3,4,1,2] => [1,4,2,3] => [2,4,1,3] => 2
[[3,3],[4,4]]
=> [3,4,1,2] => [1,4,2,3] => [2,4,1,3] => 2
[[1],[2],[3],[4]]
=> [4,3,2,1] => [2,4,1,3] => [4,2,1,3] => 1
[[1,1],[2,2],[3]]
=> [5,3,4,1,2] => [1,2,4,5,3] => [2,3,1,4,5] => ? = 2
[[1,1],[2,3],[3]]
=> [4,3,5,1,2] => [5,1,4,2,3] => [3,5,1,4,2] => ? = 2
[[1,2],[2,3],[3]]
=> [4,2,5,1,3] => [5,1,3,2,4] => [3,5,4,1,2] => ? = 2
[[1,1,1],[2,2,2]]
=> [4,5,6,1,2,3] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => ? = 2
[[1],[7]]
=> [2,1] => [2,1] => [1,2] => 1
[[2],[7]]
=> [2,1] => [2,1] => [1,2] => 1
[[3],[7]]
=> [2,1] => [2,1] => [1,2] => 1
[[4],[7]]
=> [2,1] => [2,1] => [1,2] => 1
[[1,1],[2,2],[4]]
=> [5,3,4,1,2] => [1,2,4,5,3] => [2,3,1,4,5] => ? = 2
[[1,1],[2,3],[4]]
=> [5,3,4,1,2] => [1,2,4,5,3] => [2,3,1,4,5] => ? = 2
[[1,1],[2,4],[3]]
=> [4,3,5,1,2] => [5,1,4,2,3] => [3,5,1,4,2] => ? = 2
[[1,1],[2,4],[4]]
=> [4,3,5,1,2] => [5,1,4,2,3] => [3,5,1,4,2] => ? = 2
[[1,1],[3,3],[4]]
=> [5,3,4,1,2] => [1,2,4,5,3] => [2,3,1,4,5] => ? = 2
[[1,1],[3,4],[4]]
=> [4,3,5,1,2] => [5,1,4,2,3] => [3,5,1,4,2] => ? = 2
[[1,2],[2,3],[4]]
=> [5,2,4,1,3] => [1,2,3,5,4] => [2,3,4,1,5] => ? = 1
[[1,2],[2,4],[3]]
=> [4,2,5,1,3] => [5,1,3,2,4] => [3,5,4,1,2] => ? = 2
[[1,2],[2,4],[4]]
=> [4,2,5,1,3] => [5,1,3,2,4] => [3,5,4,1,2] => ? = 2
[[1,2],[3,3],[4]]
=> [5,3,4,1,2] => [1,2,4,5,3] => [2,3,1,4,5] => ? = 2
[[1,3],[2,4],[3]]
=> [3,2,5,1,4] => [4,1,3,2,5] => [3,5,4,2,1] => ? = 2
[[1,2],[3,4],[4]]
=> [4,3,5,1,2] => [5,1,4,2,3] => [3,5,1,4,2] => ? = 2
[[1,3],[2,4],[4]]
=> [4,2,5,1,3] => [5,1,3,2,4] => [3,5,4,1,2] => ? = 2
[[1,3],[3,4],[4]]
=> [4,2,5,1,3] => [5,1,3,2,4] => [3,5,4,1,2] => ? = 2
[[2,2],[3,3],[4]]
=> [5,3,4,1,2] => [1,2,4,5,3] => [2,3,1,4,5] => ? = 2
[[2,2],[3,4],[4]]
=> [4,3,5,1,2] => [5,1,4,2,3] => [3,5,1,4,2] => ? = 2
[[2,3],[3,4],[4]]
=> [4,2,5,1,3] => [5,1,3,2,4] => [3,5,4,1,2] => ? = 2
[[1,1,1],[2,2,3]]
=> [4,5,6,1,2,3] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => ? = 2
[[1,1,1],[2,3,3]]
=> [4,5,6,1,2,3] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => ? = 2
[[1,1,1],[3,3,3]]
=> [4,5,6,1,2,3] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => ? = 2
[[1,1,2],[2,2,3]]
=> [3,4,6,1,2,5] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => ? = 1
[[1,1,2],[2,3,3]]
=> [3,5,6,1,2,4] => [1,4,6,2,3,5] => [2,5,6,3,1,4] => ? = 2
[[1,1,2],[3,3,3]]
=> [4,5,6,1,2,3] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => ? = 2
[[1,2,2],[2,3,3]]
=> [2,5,6,1,3,4] => [1,3,6,2,4,5] => [2,5,3,6,1,4] => ? = 2
[[1,2,2],[3,3,3]]
=> [4,5,6,1,2,3] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => ? = 2
[[2,2,2],[3,3,3]]
=> [4,5,6,1,2,3] => [1,5,6,2,3,4] => [2,5,6,1,3,4] => ? = 2
[[1,1,2],[2,3],[3]]
=> [5,3,6,1,2,4] => [6,1,4,2,3,5] => [3,5,6,4,1,2] => ? = 3
[[1,2,2],[2,3],[3]]
=> [5,2,6,1,3,4] => [6,1,3,2,4,5] => [3,5,4,6,1,2] => ? = 2
[[1,1],[2,2],[3,3]]
=> [5,6,3,4,1,2] => [6,1,2,4,5,3] => [3,4,1,5,6,2] => ? = 2
[[1,1],[2,2],[5]]
=> [5,3,4,1,2] => [1,2,4,5,3] => [2,3,1,4,5] => ? = 2
[[1,1],[2,3],[5]]
=> [5,3,4,1,2] => [1,2,4,5,3] => [2,3,1,4,5] => ? = 2
[[1,1],[2,5],[3]]
=> [4,3,5,1,2] => [5,1,4,2,3] => [3,5,1,4,2] => ? = 2
[[1,1],[2,4],[5]]
=> [5,3,4,1,2] => [1,2,4,5,3] => [2,3,1,4,5] => ? = 2
[[1,1],[2,5],[4]]
=> [4,3,5,1,2] => [5,1,4,2,3] => [3,5,1,4,2] => ? = 2
[[1,1],[2,5],[5]]
=> [4,3,5,1,2] => [5,1,4,2,3] => [3,5,1,4,2] => ? = 2
[[1,1],[3,3],[5]]
=> [5,3,4,1,2] => [1,2,4,5,3] => [2,3,1,4,5] => ? = 2
[[1,1],[3,4],[5]]
=> [5,3,4,1,2] => [1,2,4,5,3] => [2,3,1,4,5] => ? = 2
[[1,1],[3,5],[4]]
=> [4,3,5,1,2] => [5,1,4,2,3] => [3,5,1,4,2] => ? = 2
[[1,1],[3,5],[5]]
=> [4,3,5,1,2] => [5,1,4,2,3] => [3,5,1,4,2] => ? = 2
[[1,1],[4,4],[5]]
=> [5,3,4,1,2] => [1,2,4,5,3] => [2,3,1,4,5] => ? = 2
[[1,1],[4,5],[5]]
=> [4,3,5,1,2] => [5,1,4,2,3] => [3,5,1,4,2] => ? = 2
[[1,2],[2,3],[5]]
=> [5,2,4,1,3] => [1,2,3,5,4] => [2,3,4,1,5] => ? = 1
[[1,2],[2,5],[3]]
=> [4,2,5,1,3] => [5,1,3,2,4] => [3,5,4,1,2] => ? = 2
[[1,2],[2,4],[5]]
=> [5,2,4,1,3] => [1,2,3,5,4] => [2,3,4,1,5] => ? = 1
[[1,2],[2,5],[4]]
=> [4,2,5,1,3] => [5,1,3,2,4] => [3,5,4,1,2] => ? = 2
[[1,2],[2,5],[5]]
=> [4,2,5,1,3] => [5,1,3,2,4] => [3,5,4,1,2] => ? = 2
Description
The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order.
Matching statistic: St001583
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00325: Permutations —ones to leading⟶ Permutations
St001583: Permutations ⟶ ℤResult quality: 48% ●values known / values provided: 48%●distinct values known / distinct values provided: 50%
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00325: Permutations —ones to leading⟶ Permutations
St001583: Permutations ⟶ ℤResult quality: 48% ●values known / values provided: 48%●distinct values known / distinct values provided: 50%
Values
[[1],[2]]
=> [2,1] => [1,2] => [1,2] => 1
[[1],[3]]
=> [2,1] => [1,2] => [1,2] => 1
[[2],[3]]
=> [2,1] => [1,2] => [1,2] => 1
[[1],[4]]
=> [2,1] => [1,2] => [1,2] => 1
[[2],[4]]
=> [2,1] => [1,2] => [1,2] => 1
[[3],[4]]
=> [2,1] => [1,2] => [1,2] => 1
[[1],[2],[3]]
=> [3,2,1] => [1,3,2] => [2,3,1] => 1
[[1,1],[2,2]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,3,2] => 2
[[1],[5]]
=> [2,1] => [1,2] => [1,2] => 1
[[2],[5]]
=> [2,1] => [1,2] => [1,2] => 1
[[3],[5]]
=> [2,1] => [1,2] => [1,2] => 1
[[4],[5]]
=> [2,1] => [1,2] => [1,2] => 1
[[1],[2],[4]]
=> [3,2,1] => [1,3,2] => [2,3,1] => 1
[[1],[3],[4]]
=> [3,2,1] => [1,3,2] => [2,3,1] => 1
[[2],[3],[4]]
=> [3,2,1] => [1,3,2] => [2,3,1] => 1
[[1,1],[2,3]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,3,2] => 2
[[1,1],[3,3]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,3,2] => 2
[[1,2],[2,3]]
=> [2,4,1,3] => [4,2,1,3] => [4,2,3,1] => 1
[[1,2],[3,3]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,3,2] => 2
[[2,2],[3,3]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,3,2] => 2
[[1],[6]]
=> [2,1] => [1,2] => [1,2] => 1
[[2],[6]]
=> [2,1] => [1,2] => [1,2] => 1
[[3],[6]]
=> [2,1] => [1,2] => [1,2] => 1
[[4],[6]]
=> [2,1] => [1,2] => [1,2] => 1
[[5],[6]]
=> [2,1] => [1,2] => [1,2] => 1
[[1],[2],[5]]
=> [3,2,1] => [1,3,2] => [2,3,1] => 1
[[1],[3],[5]]
=> [3,2,1] => [1,3,2] => [2,3,1] => 1
[[1],[4],[5]]
=> [3,2,1] => [1,3,2] => [2,3,1] => 1
[[2],[3],[5]]
=> [3,2,1] => [1,3,2] => [2,3,1] => 1
[[2],[4],[5]]
=> [3,2,1] => [1,3,2] => [2,3,1] => 1
[[3],[4],[5]]
=> [3,2,1] => [1,3,2] => [2,3,1] => 1
[[1,1],[2,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,3,2] => 2
[[1,1],[3,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,3,2] => 2
[[1,1],[4,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,3,2] => 2
[[1,2],[2,4]]
=> [2,4,1,3] => [4,2,1,3] => [4,2,3,1] => 1
[[1,2],[3,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,3,2] => 2
[[1,3],[2,4]]
=> [2,4,1,3] => [4,2,1,3] => [4,2,3,1] => 1
[[1,2],[4,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,3,2] => 2
[[1,3],[3,4]]
=> [2,4,1,3] => [4,2,1,3] => [4,2,3,1] => 1
[[1,3],[4,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,3,2] => 2
[[2,2],[3,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,3,2] => 2
[[2,2],[4,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,3,2] => 2
[[2,3],[3,4]]
=> [2,4,1,3] => [4,2,1,3] => [4,2,3,1] => 1
[[2,3],[4,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,3,2] => 2
[[3,3],[4,4]]
=> [3,4,1,2] => [4,1,2,3] => [4,1,3,2] => 2
[[1],[2],[3],[4]]
=> [4,3,2,1] => [1,4,3,2] => [3,4,2,1] => 1
[[1,1],[2,2],[3]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,1],[2,3],[3]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,4,3,2] => ? = 2
[[1,2],[2,3],[3]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,2,4,3,1] => ? = 2
[[1,1,1],[2,2,2]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,1,6,4,2,3] => ? = 2
[[1],[7]]
=> [2,1] => [1,2] => [1,2] => 1
[[2],[7]]
=> [2,1] => [1,2] => [1,2] => 1
[[3],[7]]
=> [2,1] => [1,2] => [1,2] => 1
[[4],[7]]
=> [2,1] => [1,2] => [1,2] => 1
[[1,1],[2,2],[4]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,1],[2,3],[4]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,1],[2,4],[3]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,4,3,2] => ? = 2
[[1,1],[2,4],[4]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,4,3,2] => ? = 2
[[1,1],[3,3],[4]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,1],[3,4],[4]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,4,3,2] => ? = 2
[[1,2],[2,3],[4]]
=> [5,2,4,1,3] => [5,3,1,4,2] => [5,2,3,4,1] => ? = 1
[[1,2],[2,4],[3]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,2,4,3,1] => ? = 2
[[1,2],[2,4],[4]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,2,4,3,1] => ? = 2
[[1,2],[3,3],[4]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,3],[2,4],[3]]
=> [3,2,5,1,4] => [5,3,2,1,4] => [5,3,4,2,1] => ? = 2
[[1,2],[3,4],[4]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,4,3,2] => ? = 2
[[1,3],[2,4],[4]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,2,4,3,1] => ? = 2
[[1,3],[3,4],[4]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,2,4,3,1] => ? = 2
[[2,2],[3,3],[4]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[2,2],[3,4],[4]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,4,3,2] => ? = 2
[[2,3],[3,4],[4]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,2,4,3,1] => ? = 2
[[1,1,1],[2,2,3]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,1,6,4,2,3] => ? = 2
[[1,1,1],[2,3,3]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,1,6,4,2,3] => ? = 2
[[1,1,1],[3,3,3]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,1,6,4,2,3] => ? = 2
[[1,1,2],[2,2,3]]
=> [3,4,6,1,2,5] => [5,6,2,3,1,4] => [5,3,6,4,1,2] => ? = 1
[[1,1,2],[2,3,3]]
=> [3,5,6,1,2,4] => [5,6,2,1,3,4] => [5,2,6,4,1,3] => ? = 2
[[1,1,2],[3,3,3]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,1,6,4,2,3] => ? = 2
[[1,2,2],[2,3,3]]
=> [2,5,6,1,3,4] => [5,2,6,1,3,4] => [4,1,5,3,6,2] => ? = 2
[[1,2,2],[3,3,3]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,1,6,4,2,3] => ? = 2
[[2,2,2],[3,3,3]]
=> [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,1,6,4,2,3] => ? = 2
[[1,1,2],[2,3],[3]]
=> [5,3,6,1,2,4] => [5,6,3,1,2,4] => [5,2,6,4,3,1] => ? = 3
[[1,2,2],[2,3],[3]]
=> [5,2,6,1,3,4] => [5,3,6,1,2,4] => [4,1,5,3,2,6] => ? = 2
[[1,1],[2,2],[3,3]]
=> [5,6,3,4,1,2] => [6,1,4,5,2,3] => [6,1,3,4,2,5] => ? = 2
[[1,1],[2,2],[5]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,1],[2,3],[5]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,1],[2,5],[3]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,4,3,2] => ? = 2
[[1,1],[2,4],[5]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,1],[2,5],[4]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,4,3,2] => ? = 2
[[1,1],[2,5],[5]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,4,3,2] => ? = 2
[[1,1],[3,3],[5]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,1],[3,4],[5]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,1],[3,5],[4]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,4,3,2] => ? = 2
[[1,1],[3,5],[5]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,4,3,2] => ? = 2
[[1,1],[4,4],[5]]
=> [5,3,4,1,2] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 2
[[1,1],[4,5],[5]]
=> [4,3,5,1,2] => [5,1,3,2,4] => [5,1,4,3,2] => ? = 2
[[1,2],[2,3],[5]]
=> [5,2,4,1,3] => [5,3,1,4,2] => [5,2,3,4,1] => ? = 1
[[1,2],[2,5],[3]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,2,4,3,1] => ? = 2
[[1,2],[2,4],[5]]
=> [5,2,4,1,3] => [5,3,1,4,2] => [5,2,3,4,1] => ? = 1
[[1,2],[2,5],[4]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,2,4,3,1] => ? = 2
[[1,2],[2,5],[5]]
=> [4,2,5,1,3] => [5,3,1,2,4] => [5,2,4,3,1] => ? = 2
Description
The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order.
Matching statistic: St000845
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000845: Posets ⟶ ℤResult quality: 41% ●values known / values provided: 41%●distinct values known / distinct values provided: 75%
Mp00209: Permutations —pattern poset⟶ Posets
St000845: Posets ⟶ ℤResult quality: 41% ●values known / values provided: 41%●distinct values known / distinct values provided: 75%
Values
[[1],[2]]
=> [2,1] => ([(0,1)],2)
=> 1
[[1],[3]]
=> [2,1] => ([(0,1)],2)
=> 1
[[2],[3]]
=> [2,1] => ([(0,1)],2)
=> 1
[[1],[4]]
=> [2,1] => ([(0,1)],2)
=> 1
[[2],[4]]
=> [2,1] => ([(0,1)],2)
=> 1
[[3],[4]]
=> [2,1] => ([(0,1)],2)
=> 1
[[1],[2],[3]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[1,1],[2,2]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[1],[5]]
=> [2,1] => ([(0,1)],2)
=> 1
[[2],[5]]
=> [2,1] => ([(0,1)],2)
=> 1
[[3],[5]]
=> [2,1] => ([(0,1)],2)
=> 1
[[4],[5]]
=> [2,1] => ([(0,1)],2)
=> 1
[[1],[2],[4]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[1],[3],[4]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[2],[3],[4]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[1,1],[2,3]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[1,1],[3,3]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[1,2],[2,3]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,2],[3,3]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[2,2],[3,3]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[1],[6]]
=> [2,1] => ([(0,1)],2)
=> 1
[[2],[6]]
=> [2,1] => ([(0,1)],2)
=> 1
[[3],[6]]
=> [2,1] => ([(0,1)],2)
=> 1
[[4],[6]]
=> [2,1] => ([(0,1)],2)
=> 1
[[5],[6]]
=> [2,1] => ([(0,1)],2)
=> 1
[[1],[2],[5]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[1],[3],[5]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[1],[4],[5]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[2],[3],[5]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[2],[4],[5]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[3],[4],[5]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[1,1],[2,4]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[1,1],[3,4]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[1,1],[4,4]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[1,2],[2,4]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,2],[3,4]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[1,3],[2,4]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,2],[4,4]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[1,3],[3,4]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,3],[4,4]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[2,2],[3,4]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[2,2],[4,4]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[2,3],[3,4]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[2,3],[4,4]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[3,3],[4,4]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[1],[2],[3],[4]]
=> [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[[1,1],[2,2],[3]]
=> [5,3,4,1,2] => ([(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],[3]]
=> [4,3,5,1,2] => ([(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)
=> ? = 2
[[1,2],[2,3],[3]]
=> [4,2,5,1,3] => ([(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
[[1,1,1],[2,2,2]]
=> [4,5,6,1,2,3] => ([(0,1),(0,2),(1,4),(1,10),(2,3),(2,10),(3,5),(3,8),(4,5),(4,9),(5,11),(7,6),(8,7),(8,11),(9,7),(9,11),(10,8),(10,9),(11,6)],12)
=> ? = 2
[[1],[7]]
=> [2,1] => ([(0,1)],2)
=> 1
[[2],[7]]
=> [2,1] => ([(0,1)],2)
=> 1
[[3],[7]]
=> [2,1] => ([(0,1)],2)
=> 1
[[4],[7]]
=> [2,1] => ([(0,1)],2)
=> 1
[[5],[7]]
=> [2,1] => ([(0,1)],2)
=> 1
[[6],[7]]
=> [2,1] => ([(0,1)],2)
=> 1
[[1],[2],[6]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[1],[3],[6]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[1],[4],[6]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[1,2],[2,5]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,3],[2,5]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,4],[2,5]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,3],[3,5]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,4],[3,5]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,4],[4,5]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[2,3],[3,5]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[2,4],[3,5]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[2,4],[4,5]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[3,4],[4,5]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,1],[2,2],[4]]
=> [5,3,4,1,2] => ([(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]]
=> [5,3,4,1,2] => ([(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],[2,4],[3]]
=> [4,3,5,1,2] => ([(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)
=> ? = 2
[[1,1],[2,4],[4]]
=> [4,3,5,1,2] => ([(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)
=> ? = 2
[[1,1],[3,3],[4]]
=> [5,3,4,1,2] => ([(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],[3,4],[4]]
=> [4,3,5,1,2] => ([(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)
=> ? = 2
[[1,2],[2,3],[4]]
=> [5,2,4,1,3] => ([(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)
=> ? = 1
[[1,2],[2,4],[3]]
=> [4,2,5,1,3] => ([(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
[[1,2],[2,4],[4]]
=> [4,2,5,1,3] => ([(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
[[1,2],[3,3],[4]]
=> [5,3,4,1,2] => ([(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
[[1,3],[2,4],[3]]
=> [3,2,5,1,4] => ([(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
[[1,2],[3,4],[4]]
=> [4,3,5,1,2] => ([(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)
=> ? = 2
[[1,3],[2,4],[4]]
=> [4,2,5,1,3] => ([(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
[[1,3],[3,4],[4]]
=> [4,2,5,1,3] => ([(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
[[2,2],[3,3],[4]]
=> [5,3,4,1,2] => ([(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
[[2,2],[3,4],[4]]
=> [4,3,5,1,2] => ([(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)
=> ? = 2
[[2,3],[3,4],[4]]
=> [4,2,5,1,3] => ([(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
[[1,1,1],[2,2,3]]
=> [4,5,6,1,2,3] => ([(0,1),(0,2),(1,4),(1,10),(2,3),(2,10),(3,5),(3,8),(4,5),(4,9),(5,11),(7,6),(8,7),(8,11),(9,7),(9,11),(10,8),(10,9),(11,6)],12)
=> ? = 2
[[1,1,1],[2,3,3]]
=> [4,5,6,1,2,3] => ([(0,1),(0,2),(1,4),(1,10),(2,3),(2,10),(3,5),(3,8),(4,5),(4,9),(5,11),(7,6),(8,7),(8,11),(9,7),(9,11),(10,8),(10,9),(11,6)],12)
=> ? = 2
[[1,1,1],[3,3,3]]
=> [4,5,6,1,2,3] => ([(0,1),(0,2),(1,4),(1,10),(2,3),(2,10),(3,5),(3,8),(4,5),(4,9),(5,11),(7,6),(8,7),(8,11),(9,7),(9,11),(10,8),(10,9),(11,6)],12)
=> ? = 2
[[1,1,2],[2,2,3]]
=> [3,4,6,1,2,5] => ([(0,3),(0,4),(0,5),(0,6),(1,12),(1,19),(2,16),(2,19),(3,8),(3,13),(4,7),(4,9),(4,13),(5,2),(5,9),(5,10),(5,13),(6,1),(6,7),(6,8),(6,10),(7,14),(7,17),(7,19),(8,17),(8,19),(9,14),(9,16),(9,19),(10,12),(10,14),(10,16),(10,17),(12,15),(12,18),(13,16),(13,17),(14,15),(14,18),(15,11),(16,15),(16,18),(17,15),(17,18),(18,11),(19,18)],20)
=> ? = 1
[[1,1,2],[2,3,3]]
=> [3,5,6,1,2,4] => ([(0,3),(0,4),(0,5),(0,6),(1,12),(1,15),(1,17),(2,11),(2,15),(2,16),(3,8),(3,13),(4,9),(4,13),(5,2),(5,8),(5,10),(5,13),(6,1),(6,9),(6,10),(6,13),(8,15),(8,16),(9,15),(9,17),(10,11),(10,12),(10,16),(10,17),(11,14),(11,18),(12,14),(12,18),(13,16),(13,17),(14,7),(15,18),(16,14),(16,18),(17,14),(17,18),(18,7)],19)
=> ? = 2
[[1,1,2],[3,3,3]]
=> [4,5,6,1,2,3] => ([(0,1),(0,2),(1,4),(1,10),(2,3),(2,10),(3,5),(3,8),(4,5),(4,9),(5,11),(7,6),(8,7),(8,11),(9,7),(9,11),(10,8),(10,9),(11,6)],12)
=> ? = 2
[[1,2,2],[2,3,3]]
=> [2,5,6,1,3,4] => ([(0,3),(0,4),(0,5),(0,6),(1,12),(1,19),(2,16),(2,19),(3,8),(3,13),(4,7),(4,9),(4,13),(5,2),(5,9),(5,10),(5,13),(6,1),(6,7),(6,8),(6,10),(7,14),(7,17),(7,19),(8,17),(8,19),(9,14),(9,16),(9,19),(10,12),(10,14),(10,16),(10,17),(12,15),(12,18),(13,16),(13,17),(14,15),(14,18),(15,11),(16,15),(16,18),(17,15),(17,18),(18,11),(19,18)],20)
=> ? = 2
[[1,2,2],[3,3,3]]
=> [4,5,6,1,2,3] => ([(0,1),(0,2),(1,4),(1,10),(2,3),(2,10),(3,5),(3,8),(4,5),(4,9),(5,11),(7,6),(8,7),(8,11),(9,7),(9,11),(10,8),(10,9),(11,6)],12)
=> ? = 2
[[2,2,2],[3,3,3]]
=> [4,5,6,1,2,3] => ([(0,1),(0,2),(1,4),(1,10),(2,3),(2,10),(3,5),(3,8),(4,5),(4,9),(5,11),(7,6),(8,7),(8,11),(9,7),(9,11),(10,8),(10,9),(11,6)],12)
=> ? = 2
[[1,1,2],[2,3],[3]]
=> [5,3,6,1,2,4] => ([(0,1),(0,3),(0,4),(0,5),(0,6),(1,16),(1,18),(2,8),(2,17),(2,19),(2,22),(3,11),(3,12),(3,18),(4,13),(4,14),(4,16),(4,18),(5,10),(5,11),(5,13),(5,16),(6,2),(6,10),(6,12),(6,14),(6,18),(7,20),(8,20),(8,21),(10,15),(10,19),(10,22),(11,15),(11,22),(12,15),(12,17),(12,19),(13,7),(13,19),(13,22),(14,8),(14,17),(14,19),(14,22),(15,21),(16,7),(16,22),(17,20),(17,21),(18,17),(18,22),(19,20),(19,21),(20,9),(21,9),(22,20),(22,21)],23)
=> ? = 3
[[1,2,2],[2,3],[3]]
=> [5,2,6,1,3,4] => ([(0,1),(0,3),(0,4),(0,5),(0,6),(1,16),(1,18),(2,7),(2,17),(2,19),(3,11),(3,12),(3,16),(3,18),(4,10),(4,13),(4,18),(5,9),(5,10),(5,12),(5,18),(6,2),(6,9),(6,11),(6,13),(6,16),(7,20),(9,15),(9,17),(9,19),(9,22),(10,14),(10,19),(11,15),(11,17),(11,19),(11,22),(12,14),(12,15),(12,22),(13,7),(13,19),(13,22),(14,21),(15,20),(15,21),(16,17),(16,22),(17,20),(17,21),(18,14),(18,22),(19,20),(19,21),(20,8),(21,8),(22,20),(22,21)],23)
=> ? = 2
[[1,1],[2,2],[3,3]]
=> [5,6,3,4,1,2] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(1,12),(2,6),(2,7),(2,12),(3,5),(3,7),(3,12),(5,9),(5,10),(6,9),(6,11),(7,9),(7,10),(7,11),(8,4),(9,13),(10,8),(10,13),(11,8),(11,13),(12,10),(12,11),(13,4)],14)
=> ? = 2
[[1,2],[2,6]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,3],[2,6]]
=> [2,4,1,3] => ([(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)
=> ? = 1
Description
The maximal number of elements covered by an element in a poset.
Matching statistic: St000846
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000846: Posets ⟶ ℤResult quality: 41% ●values known / values provided: 41%●distinct values known / distinct values provided: 75%
Mp00209: Permutations —pattern poset⟶ Posets
St000846: Posets ⟶ ℤResult quality: 41% ●values known / values provided: 41%●distinct values known / distinct values provided: 75%
Values
[[1],[2]]
=> [2,1] => ([(0,1)],2)
=> 1
[[1],[3]]
=> [2,1] => ([(0,1)],2)
=> 1
[[2],[3]]
=> [2,1] => ([(0,1)],2)
=> 1
[[1],[4]]
=> [2,1] => ([(0,1)],2)
=> 1
[[2],[4]]
=> [2,1] => ([(0,1)],2)
=> 1
[[3],[4]]
=> [2,1] => ([(0,1)],2)
=> 1
[[1],[2],[3]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[1,1],[2,2]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[1],[5]]
=> [2,1] => ([(0,1)],2)
=> 1
[[2],[5]]
=> [2,1] => ([(0,1)],2)
=> 1
[[3],[5]]
=> [2,1] => ([(0,1)],2)
=> 1
[[4],[5]]
=> [2,1] => ([(0,1)],2)
=> 1
[[1],[2],[4]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[1],[3],[4]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[2],[3],[4]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[1,1],[2,3]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[1,1],[3,3]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[1,2],[2,3]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,2],[3,3]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[2,2],[3,3]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[1],[6]]
=> [2,1] => ([(0,1)],2)
=> 1
[[2],[6]]
=> [2,1] => ([(0,1)],2)
=> 1
[[3],[6]]
=> [2,1] => ([(0,1)],2)
=> 1
[[4],[6]]
=> [2,1] => ([(0,1)],2)
=> 1
[[5],[6]]
=> [2,1] => ([(0,1)],2)
=> 1
[[1],[2],[5]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[1],[3],[5]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[1],[4],[5]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[2],[3],[5]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[2],[4],[5]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[3],[4],[5]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[1,1],[2,4]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[1,1],[3,4]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[1,1],[4,4]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[1,2],[2,4]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,2],[3,4]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[1,3],[2,4]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,2],[4,4]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[1,3],[3,4]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,3],[4,4]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[2,2],[3,4]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[2,2],[4,4]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[2,3],[3,4]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[2,3],[4,4]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[3,3],[4,4]]
=> [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2
[[1],[2],[3],[4]]
=> [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[[1,1],[2,2],[3]]
=> [5,3,4,1,2] => ([(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],[3]]
=> [4,3,5,1,2] => ([(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)
=> ? = 2
[[1,2],[2,3],[3]]
=> [4,2,5,1,3] => ([(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
[[1,1,1],[2,2,2]]
=> [4,5,6,1,2,3] => ([(0,1),(0,2),(1,4),(1,10),(2,3),(2,10),(3,5),(3,8),(4,5),(4,9),(5,11),(7,6),(8,7),(8,11),(9,7),(9,11),(10,8),(10,9),(11,6)],12)
=> ? = 2
[[1],[7]]
=> [2,1] => ([(0,1)],2)
=> 1
[[2],[7]]
=> [2,1] => ([(0,1)],2)
=> 1
[[3],[7]]
=> [2,1] => ([(0,1)],2)
=> 1
[[4],[7]]
=> [2,1] => ([(0,1)],2)
=> 1
[[5],[7]]
=> [2,1] => ([(0,1)],2)
=> 1
[[6],[7]]
=> [2,1] => ([(0,1)],2)
=> 1
[[1],[2],[6]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[1],[3],[6]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[1],[4],[6]]
=> [3,2,1] => ([(0,2),(2,1)],3)
=> 1
[[1,2],[2,5]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,3],[2,5]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,4],[2,5]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,3],[3,5]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,4],[3,5]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,4],[4,5]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[2,3],[3,5]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[2,4],[3,5]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[2,4],[4,5]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[3,4],[4,5]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,1],[2,2],[4]]
=> [5,3,4,1,2] => ([(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]]
=> [5,3,4,1,2] => ([(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],[2,4],[3]]
=> [4,3,5,1,2] => ([(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)
=> ? = 2
[[1,1],[2,4],[4]]
=> [4,3,5,1,2] => ([(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)
=> ? = 2
[[1,1],[3,3],[4]]
=> [5,3,4,1,2] => ([(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],[3,4],[4]]
=> [4,3,5,1,2] => ([(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)
=> ? = 2
[[1,2],[2,3],[4]]
=> [5,2,4,1,3] => ([(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)
=> ? = 1
[[1,2],[2,4],[3]]
=> [4,2,5,1,3] => ([(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
[[1,2],[2,4],[4]]
=> [4,2,5,1,3] => ([(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
[[1,2],[3,3],[4]]
=> [5,3,4,1,2] => ([(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
[[1,3],[2,4],[3]]
=> [3,2,5,1,4] => ([(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
[[1,2],[3,4],[4]]
=> [4,3,5,1,2] => ([(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)
=> ? = 2
[[1,3],[2,4],[4]]
=> [4,2,5,1,3] => ([(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
[[1,3],[3,4],[4]]
=> [4,2,5,1,3] => ([(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
[[2,2],[3,3],[4]]
=> [5,3,4,1,2] => ([(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
[[2,2],[3,4],[4]]
=> [4,3,5,1,2] => ([(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)
=> ? = 2
[[2,3],[3,4],[4]]
=> [4,2,5,1,3] => ([(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
[[1,1,1],[2,2,3]]
=> [4,5,6,1,2,3] => ([(0,1),(0,2),(1,4),(1,10),(2,3),(2,10),(3,5),(3,8),(4,5),(4,9),(5,11),(7,6),(8,7),(8,11),(9,7),(9,11),(10,8),(10,9),(11,6)],12)
=> ? = 2
[[1,1,1],[2,3,3]]
=> [4,5,6,1,2,3] => ([(0,1),(0,2),(1,4),(1,10),(2,3),(2,10),(3,5),(3,8),(4,5),(4,9),(5,11),(7,6),(8,7),(8,11),(9,7),(9,11),(10,8),(10,9),(11,6)],12)
=> ? = 2
[[1,1,1],[3,3,3]]
=> [4,5,6,1,2,3] => ([(0,1),(0,2),(1,4),(1,10),(2,3),(2,10),(3,5),(3,8),(4,5),(4,9),(5,11),(7,6),(8,7),(8,11),(9,7),(9,11),(10,8),(10,9),(11,6)],12)
=> ? = 2
[[1,1,2],[2,2,3]]
=> [3,4,6,1,2,5] => ([(0,3),(0,4),(0,5),(0,6),(1,12),(1,19),(2,16),(2,19),(3,8),(3,13),(4,7),(4,9),(4,13),(5,2),(5,9),(5,10),(5,13),(6,1),(6,7),(6,8),(6,10),(7,14),(7,17),(7,19),(8,17),(8,19),(9,14),(9,16),(9,19),(10,12),(10,14),(10,16),(10,17),(12,15),(12,18),(13,16),(13,17),(14,15),(14,18),(15,11),(16,15),(16,18),(17,15),(17,18),(18,11),(19,18)],20)
=> ? = 1
[[1,1,2],[2,3,3]]
=> [3,5,6,1,2,4] => ([(0,3),(0,4),(0,5),(0,6),(1,12),(1,15),(1,17),(2,11),(2,15),(2,16),(3,8),(3,13),(4,9),(4,13),(5,2),(5,8),(5,10),(5,13),(6,1),(6,9),(6,10),(6,13),(8,15),(8,16),(9,15),(9,17),(10,11),(10,12),(10,16),(10,17),(11,14),(11,18),(12,14),(12,18),(13,16),(13,17),(14,7),(15,18),(16,14),(16,18),(17,14),(17,18),(18,7)],19)
=> ? = 2
[[1,1,2],[3,3,3]]
=> [4,5,6,1,2,3] => ([(0,1),(0,2),(1,4),(1,10),(2,3),(2,10),(3,5),(3,8),(4,5),(4,9),(5,11),(7,6),(8,7),(8,11),(9,7),(9,11),(10,8),(10,9),(11,6)],12)
=> ? = 2
[[1,2,2],[2,3,3]]
=> [2,5,6,1,3,4] => ([(0,3),(0,4),(0,5),(0,6),(1,12),(1,19),(2,16),(2,19),(3,8),(3,13),(4,7),(4,9),(4,13),(5,2),(5,9),(5,10),(5,13),(6,1),(6,7),(6,8),(6,10),(7,14),(7,17),(7,19),(8,17),(8,19),(9,14),(9,16),(9,19),(10,12),(10,14),(10,16),(10,17),(12,15),(12,18),(13,16),(13,17),(14,15),(14,18),(15,11),(16,15),(16,18),(17,15),(17,18),(18,11),(19,18)],20)
=> ? = 2
[[1,2,2],[3,3,3]]
=> [4,5,6,1,2,3] => ([(0,1),(0,2),(1,4),(1,10),(2,3),(2,10),(3,5),(3,8),(4,5),(4,9),(5,11),(7,6),(8,7),(8,11),(9,7),(9,11),(10,8),(10,9),(11,6)],12)
=> ? = 2
[[2,2,2],[3,3,3]]
=> [4,5,6,1,2,3] => ([(0,1),(0,2),(1,4),(1,10),(2,3),(2,10),(3,5),(3,8),(4,5),(4,9),(5,11),(7,6),(8,7),(8,11),(9,7),(9,11),(10,8),(10,9),(11,6)],12)
=> ? = 2
[[1,1,2],[2,3],[3]]
=> [5,3,6,1,2,4] => ([(0,1),(0,3),(0,4),(0,5),(0,6),(1,16),(1,18),(2,8),(2,17),(2,19),(2,22),(3,11),(3,12),(3,18),(4,13),(4,14),(4,16),(4,18),(5,10),(5,11),(5,13),(5,16),(6,2),(6,10),(6,12),(6,14),(6,18),(7,20),(8,20),(8,21),(10,15),(10,19),(10,22),(11,15),(11,22),(12,15),(12,17),(12,19),(13,7),(13,19),(13,22),(14,8),(14,17),(14,19),(14,22),(15,21),(16,7),(16,22),(17,20),(17,21),(18,17),(18,22),(19,20),(19,21),(20,9),(21,9),(22,20),(22,21)],23)
=> ? = 3
[[1,2,2],[2,3],[3]]
=> [5,2,6,1,3,4] => ([(0,1),(0,3),(0,4),(0,5),(0,6),(1,16),(1,18),(2,7),(2,17),(2,19),(3,11),(3,12),(3,16),(3,18),(4,10),(4,13),(4,18),(5,9),(5,10),(5,12),(5,18),(6,2),(6,9),(6,11),(6,13),(6,16),(7,20),(9,15),(9,17),(9,19),(9,22),(10,14),(10,19),(11,15),(11,17),(11,19),(11,22),(12,14),(12,15),(12,22),(13,7),(13,19),(13,22),(14,21),(15,20),(15,21),(16,17),(16,22),(17,20),(17,21),(18,14),(18,22),(19,20),(19,21),(20,8),(21,8),(22,20),(22,21)],23)
=> ? = 2
[[1,1],[2,2],[3,3]]
=> [5,6,3,4,1,2] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(1,12),(2,6),(2,7),(2,12),(3,5),(3,7),(3,12),(5,9),(5,10),(6,9),(6,11),(7,9),(7,10),(7,11),(8,4),(9,13),(10,8),(10,13),(11,8),(11,13),(12,10),(12,11),(13,4)],14)
=> ? = 2
[[1,2],[2,6]]
=> [2,4,1,3] => ([(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)
=> ? = 1
[[1,3],[2,6]]
=> [2,4,1,3] => ([(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)
=> ? = 1
Description
The maximal number of elements covering an element of a poset.
The following 40 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000640The rank of the largest boolean interval in a poset. St001632The number of indecomposable injective modules I with dimExt1(I,A)=1 for the incidence algebra A of a poset. St000907The number of maximal antichains of minimal length in a poset. St000914The sum of the values of the Möbius function of a poset. St001624The breadth of a lattice. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St000259The diameter of a connected graph. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St001330The hat guessing number of a graph. St001816Eigenvalues of the top-to-random operator acting on a simple module. St000075The orbit size of a standard tableau under promotion. St000100The number of linear extensions of a poset. St000635The number of strictly order preserving maps of a poset into itself. St001890The maximum magnitude of the Möbius function of a poset. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001200The number of simple modules in eAe with projective dimension at most 2 in the corresponding Nakayama algebra A with minimal faithful projective-injective module eA. St000080The rank of the poset. St000679The pruning number of an ordered tree. St001805The maximal overlap of a cylindrical tableau associated with a semistandard tableau. St001713The difference of the first and last value in the first row of the Gelfand-Tsetlin pattern. St001926Sparre Andersen's position of the maximum of a signed permutation. St000782The indicator function of whether a given perfect matching is an L & P matching. St000101The cocharge of a semistandard tableau. St000112The sum of the entries reduced by the index of their row in a semistandard tableau. St000454The largest eigenvalue of a graph if it is integral. St000736The last entry in the first row of a semistandard tableau. St000739The first entry in the last row of a semistandard tableau. St001401The number of distinct entries in a semistandard tableau. St001621The number of atoms of a lattice. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St001408The number of maximal entries in a semistandard tableau. St001410The minimal entry of a semistandard tableau. St001877Number of indecomposable injective modules with projective dimension 2. St001407The number of minimal entries in a semistandard tableau. St001409The maximal entry of a semistandard tableau. St001875The number of simple modules with projective dimension at most 1.
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