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Your data matches 6 different statistics following compositions of up to 3 maps.
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Matching statistic: St000681
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St000681: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St000681: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2,3] => [1,2,3] => [1,0,1,0,1,0]
=> [2,1]
=> 0
[1,2,-3] => [1,2,3] => [1,0,1,0,1,0]
=> [2,1]
=> 0
[1,-2,3] => [1,2,3] => [1,0,1,0,1,0]
=> [2,1]
=> 0
[1,-2,-3] => [1,2,3] => [1,0,1,0,1,0]
=> [2,1]
=> 0
[-1,2,3] => [1,2,3] => [1,0,1,0,1,0]
=> [2,1]
=> 0
[-1,2,-3] => [1,2,3] => [1,0,1,0,1,0]
=> [2,1]
=> 0
[-1,-2,3] => [1,2,3] => [1,0,1,0,1,0]
=> [2,1]
=> 0
[-1,-2,-3] => [1,2,3] => [1,0,1,0,1,0]
=> [2,1]
=> 0
[1,3,2] => [1,3,2] => [1,0,1,1,0,0]
=> [1,1]
=> 1
[1,3,-2] => [1,3,2] => [1,0,1,1,0,0]
=> [1,1]
=> 1
[1,-3,2] => [1,3,2] => [1,0,1,1,0,0]
=> [1,1]
=> 1
[1,-3,-2] => [1,3,2] => [1,0,1,1,0,0]
=> [1,1]
=> 1
[-1,3,2] => [1,3,2] => [1,0,1,1,0,0]
=> [1,1]
=> 1
[-1,3,-2] => [1,3,2] => [1,0,1,1,0,0]
=> [1,1]
=> 1
[-1,-3,2] => [1,3,2] => [1,0,1,1,0,0]
=> [1,1]
=> 1
[-1,-3,-2] => [1,3,2] => [1,0,1,1,0,0]
=> [1,1]
=> 1
[2,1,3] => [2,1,3] => [1,1,0,0,1,0]
=> [2]
=> 1
[2,1,-3] => [2,1,3] => [1,1,0,0,1,0]
=> [2]
=> 1
[2,-1,3] => [2,1,3] => [1,1,0,0,1,0]
=> [2]
=> 1
[2,-1,-3] => [2,1,3] => [1,1,0,0,1,0]
=> [2]
=> 1
[-2,1,3] => [2,1,3] => [1,1,0,0,1,0]
=> [2]
=> 1
[-2,1,-3] => [2,1,3] => [1,1,0,0,1,0]
=> [2]
=> 1
[-2,-1,3] => [2,1,3] => [1,1,0,0,1,0]
=> [2]
=> 1
[-2,-1,-3] => [2,1,3] => [1,1,0,0,1,0]
=> [2]
=> 1
[1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 1
[1,2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 1
[1,2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 1
[1,2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 1
[1,-2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 1
[1,-2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 1
[1,-2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 1
[1,-2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 1
[-1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 1
[-1,2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 1
[-1,2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 1
[-1,2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 1
[-1,-2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 1
[-1,-2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 1
[-1,-2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 1
[-1,-2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 1
[1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [2,2,1]
=> 0
[1,2,4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [2,2,1]
=> 0
[1,2,-4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [2,2,1]
=> 0
[1,2,-4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [2,2,1]
=> 0
[1,-2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [2,2,1]
=> 0
[1,-2,4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [2,2,1]
=> 0
[1,-2,-4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [2,2,1]
=> 0
[1,-2,-4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [2,2,1]
=> 0
[-1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [2,2,1]
=> 0
[-1,2,4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [2,2,1]
=> 0
Description
The Grundy value of Chomp on Ferrers diagrams.
Players take turns and choose a cell of the diagram, cutting off all cells below and to the right of this cell in English notation. The player who is left with the single cell partition looses. The traditional version is played on chocolate bars, see [1].
This statistic is the Grundy value of the partition, that is, the smallest non-negative integer which does not occur as value of a partition obtained by a single move.
Matching statistic: St000189
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St000189: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 10%
Mp00208: Permutations —lattice of intervals⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St000189: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 10%
Values
[1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ? = 0 + 5
[1,2,-3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ? = 0 + 5
[1,-2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ? = 0 + 5
[1,-2,-3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ? = 0 + 5
[-1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ? = 0 + 5
[-1,2,-3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ? = 0 + 5
[-1,-2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ? = 0 + 5
[-1,-2,-3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ? = 0 + 5
[1,3,2] => [1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 6 = 1 + 5
[1,3,-2] => [1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 6 = 1 + 5
[1,-3,2] => [1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 6 = 1 + 5
[1,-3,-2] => [1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 6 = 1 + 5
[-1,3,2] => [1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 6 = 1 + 5
[-1,3,-2] => [1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 6 = 1 + 5
[-1,-3,2] => [1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 6 = 1 + 5
[-1,-3,-2] => [1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 6 = 1 + 5
[2,1,3] => [2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 6 = 1 + 5
[2,1,-3] => [2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 6 = 1 + 5
[2,-1,3] => [2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 6 = 1 + 5
[2,-1,-3] => [2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 6 = 1 + 5
[-2,1,3] => [2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 6 = 1 + 5
[-2,1,-3] => [2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 6 = 1 + 5
[-2,-1,3] => [2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 6 = 1 + 5
[-2,-1,-3] => [2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 6 = 1 + 5
[1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 1 + 5
[1,2,3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 1 + 5
[1,2,-3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 1 + 5
[1,2,-3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 1 + 5
[1,-2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 1 + 5
[1,-2,3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 1 + 5
[1,-2,-3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 1 + 5
[1,-2,-3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 1 + 5
[-1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 1 + 5
[-1,2,3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 1 + 5
[-1,2,-3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 1 + 5
[-1,2,-3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 1 + 5
[-1,-2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 1 + 5
[-1,-2,3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 1 + 5
[-1,-2,-3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 1 + 5
[-1,-2,-3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ? = 1 + 5
[1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 0 + 5
[1,2,4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 0 + 5
[1,2,-4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 0 + 5
[1,2,-4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 0 + 5
[1,-2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 0 + 5
[1,-2,4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 0 + 5
[1,-2,-4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 0 + 5
[1,-2,-4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 0 + 5
[-1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 0 + 5
[-1,2,4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 0 + 5
[-1,2,-4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 0 + 5
[-1,2,-4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 0 + 5
[-1,-2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 0 + 5
[-1,-2,4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 0 + 5
[-1,-2,-4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 0 + 5
[-1,-2,-4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ? = 0 + 5
[1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 0 + 5
[1,3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 0 + 5
[1,3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 0 + 5
[1,3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 0 + 5
[1,-3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 0 + 5
[1,-3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 0 + 5
[1,-3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 0 + 5
[1,-3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 0 + 5
[-1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 0 + 5
[-1,3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 0 + 5
[2,4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[2,4,1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[2,4,-1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[2,4,-1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[2,-4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[2,-4,1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[2,-4,-1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[2,-4,-1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[-2,4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[-2,4,1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[-2,4,-1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[-2,4,-1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[-2,-4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[-2,-4,1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[-2,-4,-1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[-2,-4,-1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[3,1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[3,1,4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[3,1,-4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[3,1,-4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[3,-1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[3,-1,4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[3,-1,-4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[3,-1,-4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[-3,1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[-3,1,4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[-3,1,-4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[-3,1,-4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[-3,-1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[-3,-1,4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[-3,-1,-4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
[-3,-1,-4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 6 = 1 + 5
Description
The number of elements in the poset.
Matching statistic: St000173
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00063: Permutations —to alternating sign matrix⟶ Alternating sign matrices
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
St000173: Semistandard tableaux ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 20%
Mp00063: Permutations —to alternating sign matrix⟶ Alternating sign matrices
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
St000173: Semistandard tableaux ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 20%
Values
[1,2,3] => [1,2,3] => [[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> 0
[1,2,-3] => [1,2,3] => [[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> 0
[1,-2,3] => [1,2,3] => [[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> 0
[1,-2,-3] => [1,2,3] => [[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> 0
[-1,2,3] => [1,2,3] => [[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> 0
[-1,2,-3] => [1,2,3] => [[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> 0
[-1,-2,3] => [1,2,3] => [[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> 0
[-1,-2,-3] => [1,2,3] => [[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> 0
[1,3,2] => [1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> 1
[1,3,-2] => [1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> 1
[1,-3,2] => [1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> 1
[1,-3,-2] => [1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> 1
[-1,3,2] => [1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> 1
[-1,3,-2] => [1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> 1
[-1,-3,2] => [1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> 1
[-1,-3,-2] => [1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> 1
[2,1,3] => [2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> 1
[2,1,-3] => [2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> 1
[2,-1,3] => [2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> 1
[2,-1,-3] => [2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> 1
[-2,1,3] => [2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> 1
[-2,1,-3] => [2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> 1
[-2,-1,3] => [2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> 1
[-2,-1,-3] => [2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> 1
[1,2,3,4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[1,2,3,-4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[1,2,-3,4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[1,2,-3,-4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[1,-2,3,4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[1,-2,3,-4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[1,-2,-3,4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[1,-2,-3,-4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[-1,2,3,4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[-1,2,3,-4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[-1,2,-3,4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[-1,2,-3,-4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[-1,-2,3,4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[-1,-2,3,-4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[-1,-2,-3,4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[-1,-2,-3,-4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[1,2,4,3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[1,2,4,-3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[1,2,-4,3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[1,2,-4,-3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[1,-2,4,3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[1,-2,4,-3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[1,-2,-4,3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[1,-2,-4,-3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[-1,2,4,3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[-1,2,4,-3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[-1,2,-4,3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[-1,2,-4,-3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[-1,-2,4,3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[-1,-2,4,-3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[-1,-2,-4,3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[-1,-2,-4,-3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[1,3,2,4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[1,3,2,-4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[1,3,-2,4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[1,3,-2,-4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[1,-3,2,4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[1,-3,2,-4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[1,-3,-2,4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[1,-3,-2,-4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[-1,3,2,4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[-1,3,2,-4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[-1,3,-2,4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[-1,3,-2,-4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[-1,-3,2,4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[-1,-3,2,-4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[-1,-3,-2,4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[-1,-3,-2,-4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[1,3,4,2] => [1,3,4,2] => [[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
=> [[1,1,1,1],[2,2,4],[3,4],[4]]
=> ? = 3
[1,3,4,-2] => [1,3,4,2] => [[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
=> [[1,1,1,1],[2,2,4],[3,4],[4]]
=> ? = 3
Description
The segment statistic of a semistandard tableau.
Let ''T'' be a tableau. A ''k''-segment of ''T'' (in the ''i''th row) is defined to be a maximal consecutive sequence of ''k''-boxes in the ith row. Note that the possible ''i''-boxes in the ''i''th row are not considered to be ''i''-segments. Then seg(''T'') is the total number of ''k''-segments in ''T'' as ''k'' varies over all possible values.
Matching statistic: St000174
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00063: Permutations —to alternating sign matrix⟶ Alternating sign matrices
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
St000174: Semistandard tableaux ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 20%
Mp00063: Permutations —to alternating sign matrix⟶ Alternating sign matrices
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
St000174: Semistandard tableaux ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 20%
Values
[1,2,3] => [1,2,3] => [[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> 0
[1,2,-3] => [1,2,3] => [[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> 0
[1,-2,3] => [1,2,3] => [[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> 0
[1,-2,-3] => [1,2,3] => [[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> 0
[-1,2,3] => [1,2,3] => [[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> 0
[-1,2,-3] => [1,2,3] => [[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> 0
[-1,-2,3] => [1,2,3] => [[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> 0
[-1,-2,-3] => [1,2,3] => [[1,0,0],[0,1,0],[0,0,1]]
=> [[1,1,1],[2,2],[3]]
=> 0
[1,3,2] => [1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> 1
[1,3,-2] => [1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> 1
[1,-3,2] => [1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> 1
[1,-3,-2] => [1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> 1
[-1,3,2] => [1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> 1
[-1,3,-2] => [1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> 1
[-1,-3,2] => [1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> 1
[-1,-3,-2] => [1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
=> [[1,1,1],[2,3],[3]]
=> 1
[2,1,3] => [2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> 1
[2,1,-3] => [2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> 1
[2,-1,3] => [2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> 1
[2,-1,-3] => [2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> 1
[-2,1,3] => [2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> 1
[-2,1,-3] => [2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> 1
[-2,-1,3] => [2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> 1
[-2,-1,-3] => [2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
=> [[1,1,2],[2,2],[3]]
=> 1
[1,2,3,4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[1,2,3,-4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[1,2,-3,4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[1,2,-3,-4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[1,-2,3,4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[1,-2,3,-4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[1,-2,-3,4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[1,-2,-3,-4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[-1,2,3,4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[-1,2,3,-4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[-1,2,-3,4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[-1,2,-3,-4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[-1,-2,3,4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[-1,-2,3,-4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[-1,-2,-3,4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[-1,-2,-3,-4] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,2],[3,3],[4]]
=> ? = 1
[1,2,4,3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[1,2,4,-3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[1,2,-4,3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[1,2,-4,-3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[1,-2,4,3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[1,-2,4,-3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[1,-2,-4,3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[1,-2,-4,-3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[-1,2,4,3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[-1,2,4,-3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[-1,2,-4,3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[-1,2,-4,-3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[-1,-2,4,3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[-1,-2,4,-3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[-1,-2,-4,3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[-1,-2,-4,-3] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
=> [[1,1,1,1],[2,2,2],[3,4],[4]]
=> ? = 0
[1,3,2,4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[1,3,2,-4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[1,3,-2,4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[1,3,-2,-4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[1,-3,2,4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[1,-3,2,-4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[1,-3,-2,4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[1,-3,-2,-4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[-1,3,2,4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[-1,3,2,-4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[-1,3,-2,4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[-1,3,-2,-4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[-1,-3,2,4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[-1,-3,2,-4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[-1,-3,-2,4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[-1,-3,-2,-4] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
=> [[1,1,1,1],[2,2,3],[3,3],[4]]
=> ? = 0
[1,3,4,2] => [1,3,4,2] => [[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
=> [[1,1,1,1],[2,2,4],[3,4],[4]]
=> ? = 3
[1,3,4,-2] => [1,3,4,2] => [[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
=> [[1,1,1,1],[2,2,4],[3,4],[4]]
=> ? = 3
Description
The flush statistic of a semistandard tableau.
Let $T$ be a tableaux with $r$ rows such that each row is longer than the row beneath it by at least one box. Let $1 \leq i < k \leq r+1$ and suppose $l$ is the smallest integer greater than $k$ such that there exists an $l$-segment in the $(i+1)$-st row of $T$. A $k$-segment in the $i$-th row of $T$ is called '''flush''' if the leftmost box in the $k$-segment and the leftmost box of the $l$-segment are in the same column of $T$. If, however, no such $l$ exists, then this $k$-segment is said to be flush if the number of boxes in the $k$-segment is equal to difference of the number of boxes between the $i$-th row and $(i+1)$-st row. The flush statistic is given by the number of $k$-segments in $T$.
Matching statistic: St000075
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
St000075: Standard tableaux ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 20%
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
St000075: Standard tableaux ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 20%
Values
[1,2,3] => [1,2,3] => [1,0,1,0,1,0]
=> [[1,3,5],[2,4,6]]
=> 2 = 0 + 2
[1,2,-3] => [1,2,3] => [1,0,1,0,1,0]
=> [[1,3,5],[2,4,6]]
=> 2 = 0 + 2
[1,-2,3] => [1,2,3] => [1,0,1,0,1,0]
=> [[1,3,5],[2,4,6]]
=> 2 = 0 + 2
[1,-2,-3] => [1,2,3] => [1,0,1,0,1,0]
=> [[1,3,5],[2,4,6]]
=> 2 = 0 + 2
[-1,2,3] => [1,2,3] => [1,0,1,0,1,0]
=> [[1,3,5],[2,4,6]]
=> 2 = 0 + 2
[-1,2,-3] => [1,2,3] => [1,0,1,0,1,0]
=> [[1,3,5],[2,4,6]]
=> 2 = 0 + 2
[-1,-2,3] => [1,2,3] => [1,0,1,0,1,0]
=> [[1,3,5],[2,4,6]]
=> 2 = 0 + 2
[-1,-2,-3] => [1,2,3] => [1,0,1,0,1,0]
=> [[1,3,5],[2,4,6]]
=> 2 = 0 + 2
[1,3,2] => [1,3,2] => [1,0,1,1,0,0]
=> [[1,3,4],[2,5,6]]
=> 3 = 1 + 2
[1,3,-2] => [1,3,2] => [1,0,1,1,0,0]
=> [[1,3,4],[2,5,6]]
=> 3 = 1 + 2
[1,-3,2] => [1,3,2] => [1,0,1,1,0,0]
=> [[1,3,4],[2,5,6]]
=> 3 = 1 + 2
[1,-3,-2] => [1,3,2] => [1,0,1,1,0,0]
=> [[1,3,4],[2,5,6]]
=> 3 = 1 + 2
[-1,3,2] => [1,3,2] => [1,0,1,1,0,0]
=> [[1,3,4],[2,5,6]]
=> 3 = 1 + 2
[-1,3,-2] => [1,3,2] => [1,0,1,1,0,0]
=> [[1,3,4],[2,5,6]]
=> 3 = 1 + 2
[-1,-3,2] => [1,3,2] => [1,0,1,1,0,0]
=> [[1,3,4],[2,5,6]]
=> 3 = 1 + 2
[-1,-3,-2] => [1,3,2] => [1,0,1,1,0,0]
=> [[1,3,4],[2,5,6]]
=> 3 = 1 + 2
[2,1,3] => [2,1,3] => [1,1,0,0,1,0]
=> [[1,2,5],[3,4,6]]
=> 3 = 1 + 2
[2,1,-3] => [2,1,3] => [1,1,0,0,1,0]
=> [[1,2,5],[3,4,6]]
=> 3 = 1 + 2
[2,-1,3] => [2,1,3] => [1,1,0,0,1,0]
=> [[1,2,5],[3,4,6]]
=> 3 = 1 + 2
[2,-1,-3] => [2,1,3] => [1,1,0,0,1,0]
=> [[1,2,5],[3,4,6]]
=> 3 = 1 + 2
[-2,1,3] => [2,1,3] => [1,1,0,0,1,0]
=> [[1,2,5],[3,4,6]]
=> 3 = 1 + 2
[-2,1,-3] => [2,1,3] => [1,1,0,0,1,0]
=> [[1,2,5],[3,4,6]]
=> 3 = 1 + 2
[-2,-1,3] => [2,1,3] => [1,1,0,0,1,0]
=> [[1,2,5],[3,4,6]]
=> 3 = 1 + 2
[-2,-1,-3] => [2,1,3] => [1,1,0,0,1,0]
=> [[1,2,5],[3,4,6]]
=> 3 = 1 + 2
[1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> ? = 1 + 2
[1,2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> ? = 1 + 2
[1,2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> ? = 1 + 2
[1,2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> ? = 1 + 2
[1,-2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> ? = 1 + 2
[1,-2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> ? = 1 + 2
[1,-2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> ? = 1 + 2
[1,-2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> ? = 1 + 2
[-1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> ? = 1 + 2
[-1,2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> ? = 1 + 2
[-1,2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> ? = 1 + 2
[-1,2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> ? = 1 + 2
[-1,-2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> ? = 1 + 2
[-1,-2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> ? = 1 + 2
[-1,-2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> ? = 1 + 2
[-1,-2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> ? = 1 + 2
[1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> ? = 0 + 2
[1,2,4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> ? = 0 + 2
[1,2,-4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> ? = 0 + 2
[1,2,-4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> ? = 0 + 2
[1,-2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> ? = 0 + 2
[1,-2,4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> ? = 0 + 2
[1,-2,-4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> ? = 0 + 2
[1,-2,-4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> ? = 0 + 2
[-1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> ? = 0 + 2
[-1,2,4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> ? = 0 + 2
[-1,2,-4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> ? = 0 + 2
[-1,2,-4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> ? = 0 + 2
[-1,-2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> ? = 0 + 2
[-1,-2,4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> ? = 0 + 2
[-1,-2,-4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> ? = 0 + 2
[-1,-2,-4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> ? = 0 + 2
[1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [[1,3,4,7],[2,5,6,8]]
=> ? = 0 + 2
[1,3,2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [[1,3,4,7],[2,5,6,8]]
=> ? = 0 + 2
[1,3,-2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [[1,3,4,7],[2,5,6,8]]
=> ? = 0 + 2
[1,3,-2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [[1,3,4,7],[2,5,6,8]]
=> ? = 0 + 2
[1,-3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [[1,3,4,7],[2,5,6,8]]
=> ? = 0 + 2
[1,-3,2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [[1,3,4,7],[2,5,6,8]]
=> ? = 0 + 2
[1,-3,-2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [[1,3,4,7],[2,5,6,8]]
=> ? = 0 + 2
[1,-3,-2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [[1,3,4,7],[2,5,6,8]]
=> ? = 0 + 2
[-1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [[1,3,4,7],[2,5,6,8]]
=> ? = 0 + 2
[-1,3,2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [[1,3,4,7],[2,5,6,8]]
=> ? = 0 + 2
[-1,3,-2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [[1,3,4,7],[2,5,6,8]]
=> ? = 0 + 2
[-1,3,-2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [[1,3,4,7],[2,5,6,8]]
=> ? = 0 + 2
[-1,-3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [[1,3,4,7],[2,5,6,8]]
=> ? = 0 + 2
[-1,-3,2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [[1,3,4,7],[2,5,6,8]]
=> ? = 0 + 2
[-1,-3,-2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [[1,3,4,7],[2,5,6,8]]
=> ? = 0 + 2
[-1,-3,-2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [[1,3,4,7],[2,5,6,8]]
=> ? = 0 + 2
[1,3,4,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 3 + 2
[1,3,4,-2] => [1,3,4,2] => [1,0,1,1,0,1,0,0]
=> [[1,3,4,6],[2,5,7,8]]
=> ? = 3 + 2
Description
The orbit size of a standard tableau under promotion.
Matching statistic: St001168
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001168: Permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 20%
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001168: Permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 20%
Values
[1,2,3] => [1,2,3] => [1,0,1,0,1,0]
=> [4,1,2,3] => 24 = 0 + 24
[1,2,-3] => [1,2,3] => [1,0,1,0,1,0]
=> [4,1,2,3] => 24 = 0 + 24
[1,-2,3] => [1,2,3] => [1,0,1,0,1,0]
=> [4,1,2,3] => 24 = 0 + 24
[1,-2,-3] => [1,2,3] => [1,0,1,0,1,0]
=> [4,1,2,3] => 24 = 0 + 24
[-1,2,3] => [1,2,3] => [1,0,1,0,1,0]
=> [4,1,2,3] => 24 = 0 + 24
[-1,2,-3] => [1,2,3] => [1,0,1,0,1,0]
=> [4,1,2,3] => 24 = 0 + 24
[-1,-2,3] => [1,2,3] => [1,0,1,0,1,0]
=> [4,1,2,3] => 24 = 0 + 24
[-1,-2,-3] => [1,2,3] => [1,0,1,0,1,0]
=> [4,1,2,3] => 24 = 0 + 24
[1,3,2] => [1,3,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 25 = 1 + 24
[1,3,-2] => [1,3,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 25 = 1 + 24
[1,-3,2] => [1,3,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 25 = 1 + 24
[1,-3,-2] => [1,3,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 25 = 1 + 24
[-1,3,2] => [1,3,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 25 = 1 + 24
[-1,3,-2] => [1,3,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 25 = 1 + 24
[-1,-3,2] => [1,3,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 25 = 1 + 24
[-1,-3,-2] => [1,3,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 25 = 1 + 24
[2,1,3] => [2,1,3] => [1,1,0,0,1,0]
=> [2,4,1,3] => 25 = 1 + 24
[2,1,-3] => [2,1,3] => [1,1,0,0,1,0]
=> [2,4,1,3] => 25 = 1 + 24
[2,-1,3] => [2,1,3] => [1,1,0,0,1,0]
=> [2,4,1,3] => 25 = 1 + 24
[2,-1,-3] => [2,1,3] => [1,1,0,0,1,0]
=> [2,4,1,3] => 25 = 1 + 24
[-2,1,3] => [2,1,3] => [1,1,0,0,1,0]
=> [2,4,1,3] => 25 = 1 + 24
[-2,1,-3] => [2,1,3] => [1,1,0,0,1,0]
=> [2,4,1,3] => 25 = 1 + 24
[-2,-1,3] => [2,1,3] => [1,1,0,0,1,0]
=> [2,4,1,3] => 25 = 1 + 24
[-2,-1,-3] => [2,1,3] => [1,1,0,0,1,0]
=> [2,4,1,3] => 25 = 1 + 24
[1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => ? = 1 + 24
[1,2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => ? = 1 + 24
[1,2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => ? = 1 + 24
[1,2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => ? = 1 + 24
[1,-2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => ? = 1 + 24
[1,-2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => ? = 1 + 24
[1,-2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => ? = 1 + 24
[1,-2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => ? = 1 + 24
[-1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => ? = 1 + 24
[-1,2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => ? = 1 + 24
[-1,2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => ? = 1 + 24
[-1,2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => ? = 1 + 24
[-1,-2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => ? = 1 + 24
[-1,-2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => ? = 1 + 24
[-1,-2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => ? = 1 + 24
[-1,-2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => ? = 1 + 24
[1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 0 + 24
[1,2,4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 0 + 24
[1,2,-4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 0 + 24
[1,2,-4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 0 + 24
[1,-2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 0 + 24
[1,-2,4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 0 + 24
[1,-2,-4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 0 + 24
[1,-2,-4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 0 + 24
[-1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 0 + 24
[-1,2,4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 0 + 24
[-1,2,-4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 0 + 24
[-1,2,-4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 0 + 24
[-1,-2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 0 + 24
[-1,-2,4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 0 + 24
[-1,-2,-4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 0 + 24
[-1,-2,-4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => ? = 0 + 24
[1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 0 + 24
[1,3,2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 0 + 24
[1,3,-2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 0 + 24
[1,3,-2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 0 + 24
[1,-3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 0 + 24
[1,-3,2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 0 + 24
[1,-3,-2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 0 + 24
[1,-3,-2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 0 + 24
[-1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 0 + 24
[-1,3,2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 0 + 24
[-1,3,-2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 0 + 24
[-1,3,-2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 0 + 24
[-1,-3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 0 + 24
[-1,-3,2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 0 + 24
[-1,-3,-2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 0 + 24
[-1,-3,-2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => ? = 0 + 24
[1,3,4,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 3 + 24
[1,3,4,-2] => [1,3,4,2] => [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 3 + 24
Description
The vector space dimension of the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$.
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