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Your data matches 8 different statistics following compositions of up to 3 maps.
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Matching statistic: St001683
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Mp00223: Permutations —runsort⟶ Permutations
Mp00329: Permutations —Tanimoto⟶ Permutations
St001683: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00329: Permutations —Tanimoto⟶ Permutations
St001683: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [1] => [1] => 0
[1,2] => [1,2] => [1,2] => 0
[2,1] => [1,2] => [1,2] => 0
[1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [2,1,3] => 0
[2,1,3] => [1,3,2] => [2,1,3] => 0
[2,3,1] => [1,2,3] => [1,2,3] => 0
[3,1,2] => [1,2,3] => [1,2,3] => 0
[3,2,1] => [1,2,3] => [1,2,3] => 0
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => [2,3,1,4] => 0
[1,3,2,4] => [1,3,2,4] => [1,2,4,3] => 1
[1,3,4,2] => [1,3,4,2] => [2,4,1,3] => 1
[1,4,2,3] => [1,4,2,3] => [2,1,3,4] => 0
[1,4,3,2] => [1,4,2,3] => [2,1,3,4] => 0
[2,1,3,4] => [1,3,4,2] => [2,4,1,3] => 1
[2,1,4,3] => [1,4,2,3] => [2,1,3,4] => 0
[2,3,1,4] => [1,4,2,3] => [2,1,3,4] => 0
[2,3,4,1] => [1,2,3,4] => [1,2,3,4] => 0
[2,4,1,3] => [1,3,2,4] => [1,2,4,3] => 1
[2,4,3,1] => [1,2,4,3] => [2,3,1,4] => 0
[3,1,2,4] => [1,2,4,3] => [2,3,1,4] => 0
[3,1,4,2] => [1,4,2,3] => [2,1,3,4] => 0
[3,2,1,4] => [1,4,2,3] => [2,1,3,4] => 0
[3,2,4,1] => [1,2,4,3] => [2,3,1,4] => 0
[3,4,1,2] => [1,2,3,4] => [1,2,3,4] => 0
[3,4,2,1] => [1,2,3,4] => [1,2,3,4] => 0
[4,1,2,3] => [1,2,3,4] => [1,2,3,4] => 0
[4,1,3,2] => [1,3,2,4] => [1,2,4,3] => 1
[4,2,1,3] => [1,3,2,4] => [1,2,4,3] => 1
[4,2,3,1] => [1,2,3,4] => [1,2,3,4] => 0
[4,3,1,2] => [1,2,3,4] => [1,2,3,4] => 0
[4,3,2,1] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,2,3,5,4] => [1,2,3,5,4] => [2,3,4,1,5] => 0
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,3,5,4] => 1
[1,2,4,5,3] => [1,2,4,5,3] => [2,3,5,1,4] => 1
[1,2,5,3,4] => [1,2,5,3,4] => [2,3,1,4,5] => 0
[1,2,5,4,3] => [1,2,5,3,4] => [2,3,1,4,5] => 0
[1,3,2,4,5] => [1,3,2,4,5] => [1,2,4,3,5] => 1
[1,3,2,5,4] => [1,3,2,5,4] => [2,4,3,1,5] => 1
[1,3,4,2,5] => [1,3,4,2,5] => [1,2,4,5,3] => 2
[1,3,4,5,2] => [1,3,4,5,2] => [2,4,5,1,3] => 2
[1,3,5,2,4] => [1,3,5,2,4] => [2,4,1,3,5] => 1
[1,3,5,4,2] => [1,3,5,2,4] => [2,4,1,3,5] => 1
[1,4,2,3,5] => [1,4,2,3,5] => [1,2,5,3,4] => 1
[1,4,2,5,3] => [1,4,2,5,3] => [2,5,3,1,4] => 1
[1,4,3,2,5] => [1,4,2,5,3] => [2,5,3,1,4] => 1
[1,4,3,5,2] => [1,4,2,3,5] => [1,2,5,3,4] => 1
[1,4,5,2,3] => [1,4,5,2,3] => [2,5,1,3,4] => 1
Description
The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation.
Matching statistic: St000316
Mp00223: Permutations —runsort⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
St000316: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00252: Permutations —restriction⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
St000316: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [1] => [] => [] => ? = 0
[1,2] => [1,2] => [1] => [1] => 0
[2,1] => [1,2] => [1] => [1] => 0
[1,2,3] => [1,2,3] => [1,2] => [1,2] => 0
[1,3,2] => [1,3,2] => [1,2] => [1,2] => 0
[2,1,3] => [1,3,2] => [1,2] => [1,2] => 0
[2,3,1] => [1,2,3] => [1,2] => [1,2] => 0
[3,1,2] => [1,2,3] => [1,2] => [1,2] => 0
[3,2,1] => [1,2,3] => [1,2] => [1,2] => 0
[1,2,3,4] => [1,2,3,4] => [1,2,3] => [1,2,3] => 0
[1,2,4,3] => [1,2,4,3] => [1,2,3] => [1,2,3] => 0
[1,3,2,4] => [1,3,2,4] => [1,3,2] => [1,3,2] => 1
[1,3,4,2] => [1,3,4,2] => [1,3,2] => [1,3,2] => 1
[1,4,2,3] => [1,4,2,3] => [1,2,3] => [1,2,3] => 0
[1,4,3,2] => [1,4,2,3] => [1,2,3] => [1,2,3] => 0
[2,1,3,4] => [1,3,4,2] => [1,3,2] => [1,3,2] => 1
[2,1,4,3] => [1,4,2,3] => [1,2,3] => [1,2,3] => 0
[2,3,1,4] => [1,4,2,3] => [1,2,3] => [1,2,3] => 0
[2,3,4,1] => [1,2,3,4] => [1,2,3] => [1,2,3] => 0
[2,4,1,3] => [1,3,2,4] => [1,3,2] => [1,3,2] => 1
[2,4,3,1] => [1,2,4,3] => [1,2,3] => [1,2,3] => 0
[3,1,2,4] => [1,2,4,3] => [1,2,3] => [1,2,3] => 0
[3,1,4,2] => [1,4,2,3] => [1,2,3] => [1,2,3] => 0
[3,2,1,4] => [1,4,2,3] => [1,2,3] => [1,2,3] => 0
[3,2,4,1] => [1,2,4,3] => [1,2,3] => [1,2,3] => 0
[3,4,1,2] => [1,2,3,4] => [1,2,3] => [1,2,3] => 0
[3,4,2,1] => [1,2,3,4] => [1,2,3] => [1,2,3] => 0
[4,1,2,3] => [1,2,3,4] => [1,2,3] => [1,2,3] => 0
[4,1,3,2] => [1,3,2,4] => [1,3,2] => [1,3,2] => 1
[4,2,1,3] => [1,3,2,4] => [1,3,2] => [1,3,2] => 1
[4,2,3,1] => [1,2,3,4] => [1,2,3] => [1,2,3] => 0
[4,3,1,2] => [1,2,3,4] => [1,2,3] => [1,2,3] => 0
[4,3,2,1] => [1,2,3,4] => [1,2,3] => [1,2,3] => 0
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3] => [1,2,4,3] => 1
[1,2,4,5,3] => [1,2,4,5,3] => [1,2,4,3] => [1,2,4,3] => 1
[1,2,5,3,4] => [1,2,5,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,5,4,3] => [1,2,5,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4] => [1,3,2,4] => 1
[1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,4] => [1,3,2,4] => 1
[1,3,4,2,5] => [1,3,4,2,5] => [1,3,4,2] => [1,4,2,3] => 2
[1,3,4,5,2] => [1,3,4,5,2] => [1,3,4,2] => [1,4,2,3] => 2
[1,3,5,2,4] => [1,3,5,2,4] => [1,3,2,4] => [1,3,2,4] => 1
[1,3,5,4,2] => [1,3,5,2,4] => [1,3,2,4] => [1,3,2,4] => 1
[1,4,2,3,5] => [1,4,2,3,5] => [1,4,2,3] => [1,3,4,2] => 1
[1,4,2,5,3] => [1,4,2,5,3] => [1,4,2,3] => [1,3,4,2] => 1
[1,4,3,2,5] => [1,4,2,5,3] => [1,4,2,3] => [1,3,4,2] => 1
[1,4,3,5,2] => [1,4,2,3,5] => [1,4,2,3] => [1,3,4,2] => 1
[1,4,5,2,3] => [1,4,5,2,3] => [1,4,2,3] => [1,3,4,2] => 1
[1,4,5,3,2] => [1,4,5,2,3] => [1,4,2,3] => [1,3,4,2] => 1
Description
The number of non-left-to-right-maxima of a permutation.
An integer $\sigma_i$ in the one-line notation of a permutation $\sigma$ is a **non-left-to-right-maximum** if there exists a $j < i$ such that $\sigma_j > \sigma_i$.
Matching statistic: St001964
Mp00223: Permutations —runsort⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001964: Posets ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 20%
Mp00209: Permutations —pattern poset⟶ Posets
St001964: Posets ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 20%
Values
[1] => [1] => ([],1)
=> 0
[1,2] => [1,2] => ([(0,1)],2)
=> 0
[2,1] => [1,2] => ([(0,1)],2)
=> 0
[1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 0
[1,3,2] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0
[2,1,3] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0
[2,3,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 0
[3,1,2] => [1,2,3] => ([(0,2),(2,1)],3)
=> 0
[3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 0
[1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 0
[1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 0
[1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 1
[1,3,4,2] => [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
[1,4,2,3] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 0
[1,4,3,2] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 0
[2,1,3,4] => [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
[2,1,4,3] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 0
[2,3,1,4] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 0
[2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 0
[2,4,1,3] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 1
[2,4,3,1] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 0
[3,1,2,4] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 0
[3,1,4,2] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 0
[3,2,1,4] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 0
[3,2,4,1] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 0
[3,4,1,2] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 0
[3,4,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 0
[4,1,2,3] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 0
[4,1,3,2] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 1
[4,2,1,3] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 1
[4,2,3,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 0
[4,3,1,2] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 0
[4,3,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 0
[1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 0
[1,2,4,3,5] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 1
[1,2,4,5,3] => [1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 1
[1,2,5,3,4] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0
[1,2,5,4,3] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0
[1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 1
[1,3,2,5,4] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 1
[1,3,4,2,5] => [1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 2
[1,3,4,5,2] => [1,3,4,5,2] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 2
[1,3,5,2,4] => [1,3,5,2,4] => ([(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
[1,3,5,4,2] => [1,3,5,2,4] => ([(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
[1,4,2,3,5] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 1
[1,4,2,5,3] => [1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? = 1
[1,4,3,2,5] => [1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? = 1
[1,4,3,5,2] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 1
[1,4,5,2,3] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? = 1
[1,4,5,3,2] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? = 1
[1,5,2,3,4] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0
[1,5,2,4,3] => [1,5,2,4,3] => ([(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)
=> ? = 1
[1,5,3,2,4] => [1,5,2,4,3] => ([(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)
=> ? = 1
[1,5,3,4,2] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0
[1,5,4,2,3] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0
[1,5,4,3,2] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0
[2,1,3,4,5] => [1,3,4,5,2] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 2
[2,1,3,5,4] => [1,3,5,2,4] => ([(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
[2,1,4,3,5] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 1
[2,1,4,5,3] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? = 1
[2,1,5,3,4] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0
[2,1,5,4,3] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0
[2,3,1,4,5] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? = 1
[2,3,1,5,4] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0
[2,3,4,1,5] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0
[2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[2,3,5,1,4] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 1
[2,3,5,4,1] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 0
[3,4,5,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[3,4,5,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[4,5,1,2,3] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[4,5,2,3,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[4,5,3,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[4,5,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[5,1,2,3,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[5,2,3,4,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[5,3,4,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[5,3,4,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[5,4,1,2,3] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[5,4,2,3,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[5,4,3,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[5,4,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[2,3,4,5,6,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[3,4,5,6,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[3,4,5,6,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[4,5,6,1,2,3] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[4,5,6,2,3,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[4,5,6,3,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[4,5,6,3,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[5,6,1,2,3,4] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[5,6,2,3,4,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[5,6,3,4,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[5,6,3,4,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[5,6,4,1,2,3] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[5,6,4,2,3,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[5,6,4,3,1,2] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[5,6,4,3,2,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[6,1,2,3,4,5] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
Description
The interval resolution global dimension of a poset.
This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.
Matching statistic: St000181
Mp00223: Permutations —runsort⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000181: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 20%
Mp00209: Permutations —pattern poset⟶ Posets
St000181: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 20%
Values
[1] => [1] => ([],1)
=> 1 = 0 + 1
[1,2] => [1,2] => ([(0,1)],2)
=> 1 = 0 + 1
[2,1] => [1,2] => ([(0,1)],2)
=> 1 = 0 + 1
[1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,3,2] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
[2,1,3] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
[2,3,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[3,1,2] => [1,2,3] => ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 0 + 1
[1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 1 + 1
[1,3,4,2] => [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 + 1
[1,4,2,3] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 0 + 1
[1,4,3,2] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 0 + 1
[2,1,3,4] => [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 + 1
[2,1,4,3] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 0 + 1
[2,3,1,4] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 0 + 1
[2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[2,4,1,3] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 1 + 1
[2,4,3,1] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 0 + 1
[3,1,2,4] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 0 + 1
[3,1,4,2] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 0 + 1
[3,2,1,4] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 0 + 1
[3,2,4,1] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 0 + 1
[3,4,1,2] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[3,4,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[4,1,2,3] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[4,1,3,2] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 1 + 1
[4,2,1,3] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 1 + 1
[4,2,3,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[4,3,1,2] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[4,3,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 0 + 1
[1,2,4,3,5] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 1 + 1
[1,2,4,5,3] => [1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 1 + 1
[1,2,5,3,4] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0 + 1
[1,2,5,4,3] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0 + 1
[1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 1 + 1
[1,3,2,5,4] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 1 + 1
[1,3,4,2,5] => [1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 2 + 1
[1,3,4,5,2] => [1,3,4,5,2] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 2 + 1
[1,3,5,2,4] => [1,3,5,2,4] => ([(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
[1,3,5,4,2] => [1,3,5,2,4] => ([(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
[1,4,2,3,5] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 1 + 1
[1,4,2,5,3] => [1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? = 1 + 1
[1,4,3,2,5] => [1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? = 1 + 1
[1,4,3,5,2] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 1 + 1
[1,4,5,2,3] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? = 1 + 1
[1,4,5,3,2] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? = 1 + 1
[1,5,2,3,4] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0 + 1
[1,5,2,4,3] => [1,5,2,4,3] => ([(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)
=> ? = 1 + 1
[1,5,3,2,4] => [1,5,2,4,3] => ([(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)
=> ? = 1 + 1
[1,5,3,4,2] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0 + 1
[1,5,4,2,3] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0 + 1
[1,5,4,3,2] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0 + 1
[2,1,3,4,5] => [1,3,4,5,2] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 2 + 1
[2,1,3,5,4] => [1,3,5,2,4] => ([(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
[2,1,4,3,5] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 1 + 1
[2,1,4,5,3] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? = 1 + 1
[2,1,5,3,4] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0 + 1
[2,1,5,4,3] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0 + 1
[2,3,1,4,5] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? = 1 + 1
[2,3,1,5,4] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0 + 1
[2,3,4,1,5] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0 + 1
[2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[2,3,5,1,4] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 1 + 1
[2,3,5,4,1] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 0 + 1
[3,4,5,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[3,4,5,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[4,5,1,2,3] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[4,5,2,3,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[4,5,3,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[4,5,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[5,1,2,3,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[5,2,3,4,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[5,3,4,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[5,3,4,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[5,4,1,2,3] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[5,4,2,3,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[5,4,3,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[5,4,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
Description
The number of connected components of the Hasse diagram for the poset.
Matching statistic: St001171
Mp00223: Permutations —runsort⟶ Permutations
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
St001171: Permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 40%
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
St001171: Permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 40%
Values
[1] => [1] => [1] => [1] => 0
[1,2] => [1,2] => [2,1] => [1,2] => 0
[2,1] => [1,2] => [2,1] => [1,2] => 0
[1,2,3] => [1,2,3] => [2,3,1] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [2,1,3] => [1,2,3] => 0
[2,1,3] => [1,3,2] => [2,1,3] => [1,2,3] => 0
[2,3,1] => [1,2,3] => [2,3,1] => [1,2,3] => 0
[3,1,2] => [1,2,3] => [2,3,1] => [1,2,3] => 0
[3,2,1] => [1,2,3] => [2,3,1] => [1,2,3] => 0
[1,2,3,4] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => [2,3,1,4] => [1,2,3,4] => 0
[1,3,2,4] => [1,3,2,4] => [2,4,3,1] => [1,2,4,3] => 1
[1,3,4,2] => [1,3,4,2] => [2,4,1,3] => [1,2,4,3] => 1
[1,4,2,3] => [1,4,2,3] => [2,1,4,3] => [1,2,3,4] => 0
[1,4,3,2] => [1,4,2,3] => [2,1,4,3] => [1,2,3,4] => 0
[2,1,3,4] => [1,3,4,2] => [2,4,1,3] => [1,2,4,3] => 1
[2,1,4,3] => [1,4,2,3] => [2,1,4,3] => [1,2,3,4] => 0
[2,3,1,4] => [1,4,2,3] => [2,1,4,3] => [1,2,3,4] => 0
[2,3,4,1] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[2,4,1,3] => [1,3,2,4] => [2,4,3,1] => [1,2,4,3] => 1
[2,4,3,1] => [1,2,4,3] => [2,3,1,4] => [1,2,3,4] => 0
[3,1,2,4] => [1,2,4,3] => [2,3,1,4] => [1,2,3,4] => 0
[3,1,4,2] => [1,4,2,3] => [2,1,4,3] => [1,2,3,4] => 0
[3,2,1,4] => [1,4,2,3] => [2,1,4,3] => [1,2,3,4] => 0
[3,2,4,1] => [1,2,4,3] => [2,3,1,4] => [1,2,3,4] => 0
[3,4,1,2] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[3,4,2,1] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[4,1,2,3] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[4,1,3,2] => [1,3,2,4] => [2,4,3,1] => [1,2,4,3] => 1
[4,2,1,3] => [1,3,2,4] => [2,4,3,1] => [1,2,4,3] => 1
[4,2,3,1] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[4,3,1,2] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[4,3,2,1] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[1,2,3,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => [1,2,3,4,5] => ? = 0
[1,2,3,5,4] => [1,2,3,5,4] => [2,3,4,1,5] => [1,2,3,4,5] => ? = 0
[1,2,4,3,5] => [1,2,4,3,5] => [2,3,5,4,1] => [1,2,3,5,4] => ? = 1
[1,2,4,5,3] => [1,2,4,5,3] => [2,3,5,1,4] => [1,2,3,5,4] => ? = 1
[1,2,5,3,4] => [1,2,5,3,4] => [2,3,1,5,4] => [1,2,3,4,5] => ? = 0
[1,2,5,4,3] => [1,2,5,3,4] => [2,3,1,5,4] => [1,2,3,4,5] => ? = 0
[1,3,2,4,5] => [1,3,2,4,5] => [2,4,3,5,1] => [1,2,4,5,3] => ? = 1
[1,3,2,5,4] => [1,3,2,5,4] => [2,4,3,1,5] => [1,2,4,3,5] => ? = 1
[1,3,4,2,5] => [1,3,4,2,5] => [2,4,5,3,1] => [1,2,4,3,5] => ? = 2
[1,3,4,5,2] => [1,3,4,5,2] => [2,4,5,1,3] => [1,2,4,3,5] => ? = 2
[1,3,5,2,4] => [1,3,5,2,4] => [2,4,1,5,3] => [1,2,4,5,3] => ? = 1
[1,3,5,4,2] => [1,3,5,2,4] => [2,4,1,5,3] => [1,2,4,5,3] => ? = 1
[1,4,2,3,5] => [1,4,2,3,5] => [2,5,3,4,1] => [1,2,5,3,4] => ? = 1
[1,4,2,5,3] => [1,4,2,5,3] => [2,5,3,1,4] => [1,2,5,4,3] => ? = 1
[1,4,3,2,5] => [1,4,2,5,3] => [2,5,3,1,4] => [1,2,5,4,3] => ? = 1
[1,4,3,5,2] => [1,4,2,3,5] => [2,5,3,4,1] => [1,2,5,3,4] => ? = 1
[1,4,5,2,3] => [1,4,5,2,3] => [2,5,1,4,3] => [1,2,5,3,4] => ? = 1
[1,4,5,3,2] => [1,4,5,2,3] => [2,5,1,4,3] => [1,2,5,3,4] => ? = 1
[1,5,2,3,4] => [1,5,2,3,4] => [2,1,4,5,3] => [1,2,3,4,5] => ? = 0
[1,5,2,4,3] => [1,5,2,4,3] => [2,1,4,3,5] => [1,2,3,4,5] => ? = 1
[1,5,3,2,4] => [1,5,2,4,3] => [2,1,4,3,5] => [1,2,3,4,5] => ? = 1
[1,5,3,4,2] => [1,5,2,3,4] => [2,1,4,5,3] => [1,2,3,4,5] => ? = 0
[1,5,4,2,3] => [1,5,2,3,4] => [2,1,4,5,3] => [1,2,3,4,5] => ? = 0
[1,5,4,3,2] => [1,5,2,3,4] => [2,1,4,5,3] => [1,2,3,4,5] => ? = 0
[2,1,3,4,5] => [1,3,4,5,2] => [2,4,5,1,3] => [1,2,4,3,5] => ? = 2
[2,1,3,5,4] => [1,3,5,2,4] => [2,4,1,5,3] => [1,2,4,5,3] => ? = 1
[2,1,4,3,5] => [1,4,2,3,5] => [2,5,3,4,1] => [1,2,5,3,4] => ? = 1
[2,1,4,5,3] => [1,4,5,2,3] => [2,5,1,4,3] => [1,2,5,3,4] => ? = 1
[2,1,5,3,4] => [1,5,2,3,4] => [2,1,4,5,3] => [1,2,3,4,5] => ? = 0
[2,1,5,4,3] => [1,5,2,3,4] => [2,1,4,5,3] => [1,2,3,4,5] => ? = 0
[2,3,1,4,5] => [1,4,5,2,3] => [2,5,1,4,3] => [1,2,5,3,4] => ? = 1
[2,3,1,5,4] => [1,5,2,3,4] => [2,1,4,5,3] => [1,2,3,4,5] => ? = 0
[2,3,4,1,5] => [1,5,2,3,4] => [2,1,4,5,3] => [1,2,3,4,5] => ? = 0
[2,3,4,5,1] => [1,2,3,4,5] => [2,3,4,5,1] => [1,2,3,4,5] => ? = 0
[2,3,5,1,4] => [1,4,2,3,5] => [2,5,3,4,1] => [1,2,5,3,4] => ? = 1
[2,3,5,4,1] => [1,2,3,5,4] => [2,3,4,1,5] => [1,2,3,4,5] => ? = 0
[2,4,1,3,5] => [1,3,5,2,4] => [2,4,1,5,3] => [1,2,4,5,3] => ? = 1
[2,4,1,5,3] => [1,5,2,4,3] => [2,1,4,3,5] => [1,2,3,4,5] => ? = 1
[2,4,3,1,5] => [1,5,2,4,3] => [2,1,4,3,5] => [1,2,3,4,5] => ? = 1
[2,4,3,5,1] => [1,2,4,3,5] => [2,3,5,4,1] => [1,2,3,5,4] => ? = 1
[2,4,5,1,3] => [1,3,2,4,5] => [2,4,3,5,1] => [1,2,4,5,3] => ? = 1
[2,4,5,3,1] => [1,2,4,5,3] => [2,3,5,1,4] => [1,2,3,5,4] => ? = 1
[2,5,1,3,4] => [1,3,4,2,5] => [2,4,5,3,1] => [1,2,4,3,5] => ? = 2
[2,5,1,4,3] => [1,4,2,5,3] => [2,5,3,1,4] => [1,2,5,4,3] => ? = 1
[2,5,3,1,4] => [1,4,2,5,3] => [2,5,3,1,4] => [1,2,5,4,3] => ? = 1
[2,5,3,4,1] => [1,2,5,3,4] => [2,3,1,5,4] => [1,2,3,4,5] => ? = 0
[2,5,4,1,3] => [1,3,2,5,4] => [2,4,3,1,5] => [1,2,4,3,5] => ? = 1
[2,5,4,3,1] => [1,2,5,3,4] => [2,3,1,5,4] => [1,2,3,4,5] => ? = 0
[3,1,2,4,5] => [1,2,4,5,3] => [2,3,5,1,4] => [1,2,3,5,4] => ? = 1
[3,1,2,5,4] => [1,2,5,3,4] => [2,3,1,5,4] => [1,2,3,4,5] => ? = 0
Description
The vector space dimension of $Ext_A^1(I_o,A)$ when $I_o$ is the tilting module corresponding to the permutation $o$ in the Auslander algebra $A$ of $K[x]/(x^n)$.
Matching statistic: St001890
Mp00223: Permutations —runsort⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001890: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 20%
Mp00209: Permutations —pattern poset⟶ Posets
St001890: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 20%
Values
[1] => [1] => ([],1)
=> ? = 0 + 1
[1,2] => [1,2] => ([(0,1)],2)
=> 1 = 0 + 1
[2,1] => [1,2] => ([(0,1)],2)
=> 1 = 0 + 1
[1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,3,2] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
[2,1,3] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
[2,3,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[3,1,2] => [1,2,3] => ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 0 + 1
[1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 1 + 1
[1,3,4,2] => [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 + 1
[1,4,2,3] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 0 + 1
[1,4,3,2] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 0 + 1
[2,1,3,4] => [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 + 1
[2,1,4,3] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 0 + 1
[2,3,1,4] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 0 + 1
[2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[2,4,1,3] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 1 + 1
[2,4,3,1] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 0 + 1
[3,1,2,4] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 0 + 1
[3,1,4,2] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 0 + 1
[3,2,1,4] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 0 + 1
[3,2,4,1] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 0 + 1
[3,4,1,2] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[3,4,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[4,1,2,3] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[4,1,3,2] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 1 + 1
[4,2,1,3] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 1 + 1
[4,2,3,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[4,3,1,2] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[4,3,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 0 + 1
[1,2,4,3,5] => [1,2,4,3,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 1 + 1
[1,2,4,5,3] => [1,2,4,5,3] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 1 + 1
[1,2,5,3,4] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0 + 1
[1,2,5,4,3] => [1,2,5,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0 + 1
[1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 1 + 1
[1,3,2,5,4] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 1 + 1
[1,3,4,2,5] => [1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 2 + 1
[1,3,4,5,2] => [1,3,4,5,2] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 2 + 1
[1,3,5,2,4] => [1,3,5,2,4] => ([(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
[1,3,5,4,2] => [1,3,5,2,4] => ([(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
[1,4,2,3,5] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 1 + 1
[1,4,2,5,3] => [1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? = 1 + 1
[1,4,3,2,5] => [1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
=> ? = 1 + 1
[1,4,3,5,2] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 1 + 1
[1,4,5,2,3] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? = 1 + 1
[1,4,5,3,2] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? = 1 + 1
[1,5,2,3,4] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0 + 1
[1,5,2,4,3] => [1,5,2,4,3] => ([(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)
=> ? = 1 + 1
[1,5,3,2,4] => [1,5,2,4,3] => ([(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)
=> ? = 1 + 1
[1,5,3,4,2] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0 + 1
[1,5,4,2,3] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0 + 1
[1,5,4,3,2] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0 + 1
[2,1,3,4,5] => [1,3,4,5,2] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 2 + 1
[2,1,3,5,4] => [1,3,5,2,4] => ([(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
[2,1,4,3,5] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 1 + 1
[2,1,4,5,3] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? = 1 + 1
[2,1,5,3,4] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0 + 1
[2,1,5,4,3] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0 + 1
[2,3,1,4,5] => [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
=> ? = 1 + 1
[2,3,1,5,4] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0 + 1
[2,3,4,1,5] => [1,5,2,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 0 + 1
[2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[2,3,5,1,4] => [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
=> ? = 1 + 1
[3,4,5,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[3,4,5,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[4,5,1,2,3] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[4,5,2,3,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[4,5,3,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[4,5,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[5,1,2,3,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[5,2,3,4,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[5,3,4,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[5,3,4,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[5,4,1,2,3] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[5,4,2,3,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[5,4,3,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[5,4,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
Description
The maximum magnitude of the Möbius function of a poset.
The '''Möbius function''' of a poset is the multiplicative inverse of the zeta function in the incidence algebra. The Möbius value $\mu(x, y)$ is equal to the signed sum of chains from $x$ to $y$, where odd-length chains are counted with a minus sign, so this statistic is bounded above by the total number of chains in the poset.
Matching statistic: St001207
Mp00223: Permutations —runsort⟶ Permutations
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 40%
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 40%
Values
[1] => [1] => [1] => [1] => ? = 0
[1,2] => [1,2] => [2,1] => [1,2] => 0
[2,1] => [1,2] => [2,1] => [1,2] => 0
[1,2,3] => [1,2,3] => [2,3,1] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [2,1,3] => [1,2,3] => 0
[2,1,3] => [1,3,2] => [2,1,3] => [1,2,3] => 0
[2,3,1] => [1,2,3] => [2,3,1] => [1,2,3] => 0
[3,1,2] => [1,2,3] => [2,3,1] => [1,2,3] => 0
[3,2,1] => [1,2,3] => [2,3,1] => [1,2,3] => 0
[1,2,3,4] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => [2,3,1,4] => [1,2,3,4] => 0
[1,3,2,4] => [1,3,2,4] => [2,4,3,1] => [1,2,4,3] => 1
[1,3,4,2] => [1,3,4,2] => [2,4,1,3] => [1,2,4,3] => 1
[1,4,2,3] => [1,4,2,3] => [2,1,4,3] => [1,2,3,4] => 0
[1,4,3,2] => [1,4,2,3] => [2,1,4,3] => [1,2,3,4] => 0
[2,1,3,4] => [1,3,4,2] => [2,4,1,3] => [1,2,4,3] => 1
[2,1,4,3] => [1,4,2,3] => [2,1,4,3] => [1,2,3,4] => 0
[2,3,1,4] => [1,4,2,3] => [2,1,4,3] => [1,2,3,4] => 0
[2,3,4,1] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[2,4,1,3] => [1,3,2,4] => [2,4,3,1] => [1,2,4,3] => 1
[2,4,3,1] => [1,2,4,3] => [2,3,1,4] => [1,2,3,4] => 0
[3,1,2,4] => [1,2,4,3] => [2,3,1,4] => [1,2,3,4] => 0
[3,1,4,2] => [1,4,2,3] => [2,1,4,3] => [1,2,3,4] => 0
[3,2,1,4] => [1,4,2,3] => [2,1,4,3] => [1,2,3,4] => 0
[3,2,4,1] => [1,2,4,3] => [2,3,1,4] => [1,2,3,4] => 0
[3,4,1,2] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[3,4,2,1] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[4,1,2,3] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[4,1,3,2] => [1,3,2,4] => [2,4,3,1] => [1,2,4,3] => 1
[4,2,1,3] => [1,3,2,4] => [2,4,3,1] => [1,2,4,3] => 1
[4,2,3,1] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[4,3,1,2] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[4,3,2,1] => [1,2,3,4] => [2,3,4,1] => [1,2,3,4] => 0
[1,2,3,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => [1,2,3,4,5] => ? = 0
[1,2,3,5,4] => [1,2,3,5,4] => [2,3,4,1,5] => [1,2,3,4,5] => ? = 0
[1,2,4,3,5] => [1,2,4,3,5] => [2,3,5,4,1] => [1,2,3,5,4] => ? = 1
[1,2,4,5,3] => [1,2,4,5,3] => [2,3,5,1,4] => [1,2,3,5,4] => ? = 1
[1,2,5,3,4] => [1,2,5,3,4] => [2,3,1,5,4] => [1,2,3,4,5] => ? = 0
[1,2,5,4,3] => [1,2,5,3,4] => [2,3,1,5,4] => [1,2,3,4,5] => ? = 0
[1,3,2,4,5] => [1,3,2,4,5] => [2,4,3,5,1] => [1,2,4,5,3] => ? = 1
[1,3,2,5,4] => [1,3,2,5,4] => [2,4,3,1,5] => [1,2,4,3,5] => ? = 1
[1,3,4,2,5] => [1,3,4,2,5] => [2,4,5,3,1] => [1,2,4,3,5] => ? = 2
[1,3,4,5,2] => [1,3,4,5,2] => [2,4,5,1,3] => [1,2,4,3,5] => ? = 2
[1,3,5,2,4] => [1,3,5,2,4] => [2,4,1,5,3] => [1,2,4,5,3] => ? = 1
[1,3,5,4,2] => [1,3,5,2,4] => [2,4,1,5,3] => [1,2,4,5,3] => ? = 1
[1,4,2,3,5] => [1,4,2,3,5] => [2,5,3,4,1] => [1,2,5,3,4] => ? = 1
[1,4,2,5,3] => [1,4,2,5,3] => [2,5,3,1,4] => [1,2,5,4,3] => ? = 1
[1,4,3,2,5] => [1,4,2,5,3] => [2,5,3,1,4] => [1,2,5,4,3] => ? = 1
[1,4,3,5,2] => [1,4,2,3,5] => [2,5,3,4,1] => [1,2,5,3,4] => ? = 1
[1,4,5,2,3] => [1,4,5,2,3] => [2,5,1,4,3] => [1,2,5,3,4] => ? = 1
[1,4,5,3,2] => [1,4,5,2,3] => [2,5,1,4,3] => [1,2,5,3,4] => ? = 1
[1,5,2,3,4] => [1,5,2,3,4] => [2,1,4,5,3] => [1,2,3,4,5] => ? = 0
[1,5,2,4,3] => [1,5,2,4,3] => [2,1,4,3,5] => [1,2,3,4,5] => ? = 1
[1,5,3,2,4] => [1,5,2,4,3] => [2,1,4,3,5] => [1,2,3,4,5] => ? = 1
[1,5,3,4,2] => [1,5,2,3,4] => [2,1,4,5,3] => [1,2,3,4,5] => ? = 0
[1,5,4,2,3] => [1,5,2,3,4] => [2,1,4,5,3] => [1,2,3,4,5] => ? = 0
[1,5,4,3,2] => [1,5,2,3,4] => [2,1,4,5,3] => [1,2,3,4,5] => ? = 0
[2,1,3,4,5] => [1,3,4,5,2] => [2,4,5,1,3] => [1,2,4,3,5] => ? = 2
[2,1,3,5,4] => [1,3,5,2,4] => [2,4,1,5,3] => [1,2,4,5,3] => ? = 1
[2,1,4,3,5] => [1,4,2,3,5] => [2,5,3,4,1] => [1,2,5,3,4] => ? = 1
[2,1,4,5,3] => [1,4,5,2,3] => [2,5,1,4,3] => [1,2,5,3,4] => ? = 1
[2,1,5,3,4] => [1,5,2,3,4] => [2,1,4,5,3] => [1,2,3,4,5] => ? = 0
[2,1,5,4,3] => [1,5,2,3,4] => [2,1,4,5,3] => [1,2,3,4,5] => ? = 0
[2,3,1,4,5] => [1,4,5,2,3] => [2,5,1,4,3] => [1,2,5,3,4] => ? = 1
[2,3,1,5,4] => [1,5,2,3,4] => [2,1,4,5,3] => [1,2,3,4,5] => ? = 0
[2,3,4,1,5] => [1,5,2,3,4] => [2,1,4,5,3] => [1,2,3,4,5] => ? = 0
[2,3,4,5,1] => [1,2,3,4,5] => [2,3,4,5,1] => [1,2,3,4,5] => ? = 0
[2,3,5,1,4] => [1,4,2,3,5] => [2,5,3,4,1] => [1,2,5,3,4] => ? = 1
[2,3,5,4,1] => [1,2,3,5,4] => [2,3,4,1,5] => [1,2,3,4,5] => ? = 0
[2,4,1,3,5] => [1,3,5,2,4] => [2,4,1,5,3] => [1,2,4,5,3] => ? = 1
[2,4,1,5,3] => [1,5,2,4,3] => [2,1,4,3,5] => [1,2,3,4,5] => ? = 1
[2,4,3,1,5] => [1,5,2,4,3] => [2,1,4,3,5] => [1,2,3,4,5] => ? = 1
[2,4,3,5,1] => [1,2,4,3,5] => [2,3,5,4,1] => [1,2,3,5,4] => ? = 1
[2,4,5,1,3] => [1,3,2,4,5] => [2,4,3,5,1] => [1,2,4,5,3] => ? = 1
[2,4,5,3,1] => [1,2,4,5,3] => [2,3,5,1,4] => [1,2,3,5,4] => ? = 1
[2,5,1,3,4] => [1,3,4,2,5] => [2,4,5,3,1] => [1,2,4,3,5] => ? = 2
[2,5,1,4,3] => [1,4,2,5,3] => [2,5,3,1,4] => [1,2,5,4,3] => ? = 1
[2,5,3,1,4] => [1,4,2,5,3] => [2,5,3,1,4] => [1,2,5,4,3] => ? = 1
[2,5,3,4,1] => [1,2,5,3,4] => [2,3,1,5,4] => [1,2,3,4,5] => ? = 0
[2,5,4,1,3] => [1,3,2,5,4] => [2,4,3,1,5] => [1,2,4,3,5] => ? = 1
[2,5,4,3,1] => [1,2,5,3,4] => [2,3,1,5,4] => [1,2,3,4,5] => ? = 0
[3,1,2,4,5] => [1,2,4,5,3] => [2,3,5,1,4] => [1,2,3,5,4] => ? = 1
Description
The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$.
Matching statistic: St001582
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00223: Permutations —runsort⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
St001582: Permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 40%
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
St001582: Permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 40%
Values
[1] => [1] => [1] => [1] => ? = 0 + 1
[1,2] => [1,2] => [1,2] => [1,2] => 1 = 0 + 1
[2,1] => [1,2] => [1,2] => [1,2] => 1 = 0 + 1
[1,2,3] => [1,2,3] => [1,2,3] => [1,3,2] => 1 = 0 + 1
[1,3,2] => [1,3,2] => [2,3,1] => [2,3,1] => 1 = 0 + 1
[2,1,3] => [1,3,2] => [2,3,1] => [2,3,1] => 1 = 0 + 1
[2,3,1] => [1,2,3] => [1,2,3] => [1,3,2] => 1 = 0 + 1
[3,1,2] => [1,2,3] => [1,2,3] => [1,3,2] => 1 = 0 + 1
[3,2,1] => [1,2,3] => [1,2,3] => [1,3,2] => 1 = 0 + 1
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,4,3,2] => 1 = 0 + 1
[1,2,4,3] => [1,2,4,3] => [2,3,4,1] => [2,4,3,1] => 1 = 0 + 1
[1,3,2,4] => [1,3,2,4] => [2,3,1,4] => [2,4,1,3] => 2 = 1 + 1
[1,3,4,2] => [1,3,4,2] => [2,4,1,3] => [2,4,1,3] => 2 = 1 + 1
[1,4,2,3] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 1 = 0 + 1
[1,4,3,2] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 1 = 0 + 1
[2,1,3,4] => [1,3,4,2] => [2,4,1,3] => [2,4,1,3] => 2 = 1 + 1
[2,1,4,3] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 1 = 0 + 1
[2,3,1,4] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 1 = 0 + 1
[2,3,4,1] => [1,2,3,4] => [1,2,3,4] => [1,4,3,2] => 1 = 0 + 1
[2,4,1,3] => [1,3,2,4] => [2,3,1,4] => [2,4,1,3] => 2 = 1 + 1
[2,4,3,1] => [1,2,4,3] => [2,3,4,1] => [2,4,3,1] => 1 = 0 + 1
[3,1,2,4] => [1,2,4,3] => [2,3,4,1] => [2,4,3,1] => 1 = 0 + 1
[3,1,4,2] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 1 = 0 + 1
[3,2,1,4] => [1,4,2,3] => [2,1,4,3] => [2,1,4,3] => 1 = 0 + 1
[3,2,4,1] => [1,2,4,3] => [2,3,4,1] => [2,4,3,1] => 1 = 0 + 1
[3,4,1,2] => [1,2,3,4] => [1,2,3,4] => [1,4,3,2] => 1 = 0 + 1
[3,4,2,1] => [1,2,3,4] => [1,2,3,4] => [1,4,3,2] => 1 = 0 + 1
[4,1,2,3] => [1,2,3,4] => [1,2,3,4] => [1,4,3,2] => 1 = 0 + 1
[4,1,3,2] => [1,3,2,4] => [2,3,1,4] => [2,4,1,3] => 2 = 1 + 1
[4,2,1,3] => [1,3,2,4] => [2,3,1,4] => [2,4,1,3] => 2 = 1 + 1
[4,2,3,1] => [1,2,3,4] => [1,2,3,4] => [1,4,3,2] => 1 = 0 + 1
[4,3,1,2] => [1,2,3,4] => [1,2,3,4] => [1,4,3,2] => 1 = 0 + 1
[4,3,2,1] => [1,2,3,4] => [1,2,3,4] => [1,4,3,2] => 1 = 0 + 1
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,5,4,3,2] => ? = 0 + 1
[1,2,3,5,4] => [1,2,3,5,4] => [2,3,4,5,1] => [2,5,4,3,1] => ? = 0 + 1
[1,2,4,3,5] => [1,2,4,3,5] => [2,3,4,1,5] => [2,5,4,1,3] => ? = 1 + 1
[1,2,4,5,3] => [1,2,4,5,3] => [2,3,5,1,4] => [2,5,4,1,3] => ? = 1 + 1
[1,2,5,3,4] => [1,2,5,3,4] => [2,3,1,5,4] => [2,5,1,4,3] => ? = 0 + 1
[1,2,5,4,3] => [1,2,5,3,4] => [2,3,1,5,4] => [2,5,1,4,3] => ? = 0 + 1
[1,3,2,4,5] => [1,3,2,4,5] => [2,3,1,4,5] => [2,5,1,4,3] => ? = 1 + 1
[1,3,2,5,4] => [1,3,2,5,4] => [3,4,2,5,1] => [3,5,2,4,1] => ? = 1 + 1
[1,3,4,2,5] => [1,3,4,2,5] => [2,4,1,3,5] => [2,5,1,4,3] => ? = 2 + 1
[1,3,4,5,2] => [1,3,4,5,2] => [2,5,1,3,4] => [2,5,1,4,3] => ? = 2 + 1
[1,3,5,2,4] => [1,3,5,2,4] => [2,1,4,5,3] => [2,1,5,4,3] => ? = 1 + 1
[1,3,5,4,2] => [1,3,5,2,4] => [2,1,4,5,3] => [2,1,5,4,3] => ? = 1 + 1
[1,4,2,3,5] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,5,4,3] => ? = 1 + 1
[1,4,2,5,3] => [1,4,2,5,3] => [3,4,5,1,2] => [3,5,4,1,2] => ? = 1 + 1
[1,4,3,2,5] => [1,4,2,5,3] => [3,4,5,1,2] => [3,5,4,1,2] => ? = 1 + 1
[1,4,3,5,2] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,5,4,3] => ? = 1 + 1
[1,4,5,2,3] => [1,4,5,2,3] => [2,1,5,3,4] => [2,1,5,4,3] => ? = 1 + 1
[1,4,5,3,2] => [1,4,5,2,3] => [2,1,5,3,4] => [2,1,5,4,3] => ? = 1 + 1
[1,5,2,3,4] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => ? = 0 + 1
[1,5,2,4,3] => [1,5,2,4,3] => [3,2,5,4,1] => [3,2,5,4,1] => ? = 1 + 1
[1,5,3,2,4] => [1,5,2,4,3] => [3,2,5,4,1] => [3,2,5,4,1] => ? = 1 + 1
[1,5,3,4,2] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => ? = 0 + 1
[1,5,4,2,3] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => ? = 0 + 1
[1,5,4,3,2] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => ? = 0 + 1
[2,1,3,4,5] => [1,3,4,5,2] => [2,5,1,3,4] => [2,5,1,4,3] => ? = 2 + 1
[2,1,3,5,4] => [1,3,5,2,4] => [2,1,4,5,3] => [2,1,5,4,3] => ? = 1 + 1
[2,1,4,3,5] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,5,4,3] => ? = 1 + 1
[2,1,4,5,3] => [1,4,5,2,3] => [2,1,5,3,4] => [2,1,5,4,3] => ? = 1 + 1
[2,1,5,3,4] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => ? = 0 + 1
[2,1,5,4,3] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => ? = 0 + 1
[2,3,1,4,5] => [1,4,5,2,3] => [2,1,5,3,4] => [2,1,5,4,3] => ? = 1 + 1
[2,3,1,5,4] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => ? = 0 + 1
[2,3,4,1,5] => [1,5,2,3,4] => [2,1,3,5,4] => [2,1,5,4,3] => ? = 0 + 1
[2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,5,4,3,2] => ? = 0 + 1
[2,3,5,1,4] => [1,4,2,3,5] => [2,1,4,3,5] => [2,1,5,4,3] => ? = 1 + 1
[2,3,5,4,1] => [1,2,3,5,4] => [2,3,4,5,1] => [2,5,4,3,1] => ? = 0 + 1
[2,4,1,3,5] => [1,3,5,2,4] => [2,1,4,5,3] => [2,1,5,4,3] => ? = 1 + 1
[2,4,1,5,3] => [1,5,2,4,3] => [3,2,5,4,1] => [3,2,5,4,1] => ? = 1 + 1
[2,4,3,1,5] => [1,5,2,4,3] => [3,2,5,4,1] => [3,2,5,4,1] => ? = 1 + 1
[2,4,3,5,1] => [1,2,4,3,5] => [2,3,4,1,5] => [2,5,4,1,3] => ? = 1 + 1
[2,4,5,1,3] => [1,3,2,4,5] => [2,3,1,4,5] => [2,5,1,4,3] => ? = 1 + 1
[2,4,5,3,1] => [1,2,4,5,3] => [2,3,5,1,4] => [2,5,4,1,3] => ? = 1 + 1
[2,5,1,3,4] => [1,3,4,2,5] => [2,4,1,3,5] => [2,5,1,4,3] => ? = 2 + 1
[2,5,1,4,3] => [1,4,2,5,3] => [3,4,5,1,2] => [3,5,4,1,2] => ? = 1 + 1
[2,5,3,1,4] => [1,4,2,5,3] => [3,4,5,1,2] => [3,5,4,1,2] => ? = 1 + 1
[2,5,3,4,1] => [1,2,5,3,4] => [2,3,1,5,4] => [2,5,1,4,3] => ? = 0 + 1
[2,5,4,1,3] => [1,3,2,5,4] => [3,4,2,5,1] => [3,5,2,4,1] => ? = 1 + 1
[2,5,4,3,1] => [1,2,5,3,4] => [2,3,1,5,4] => [2,5,1,4,3] => ? = 0 + 1
[3,1,2,4,5] => [1,2,4,5,3] => [2,3,5,1,4] => [2,5,4,1,3] => ? = 1 + 1
Description
The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order.
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