searching the database
Your data matches 4 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St000937
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000937: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000937: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2,3,4] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,2,4,3] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,3,2,4] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,3,4,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,4,2,3] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[1,4,3,2] => [1,4,3,2] => [2,1,1]
=> [1,1]
=> 1
[2,1,3,4] => [2,1,4,3] => [2,2]
=> [2]
=> 2
[2,1,4,3] => [2,1,4,3] => [2,2]
=> [2]
=> 2
[3,2,1,4] => [3,2,1,4] => [2,1,1]
=> [1,1]
=> 1
[3,4,1,2] => [3,4,1,2] => [2,2]
=> [2]
=> 2
[4,2,3,1] => [4,2,3,1] => [2,1,1]
=> [1,1]
=> 1
[4,3,2,1] => [4,3,2,1] => [2,2]
=> [2]
=> 2
[1,2,3,4,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,2,3,5,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,2,4,3,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,2,4,5,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,2,5,3,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,2,5,4,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,3,2,4,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,3,2,5,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,3,4,2,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,3,4,5,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,3,5,2,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,3,5,4,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,4,2,3,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,4,2,5,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,4,3,2,5] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,4,3,5,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,4,5,2,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,4,5,3,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,5,2,3,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,5,2,4,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,5,3,2,4] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,5,3,4,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,5,4,2,3] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[1,5,4,3,2] => [1,5,4,3,2] => [2,2,1]
=> [2,1]
=> 1
[2,1,3,4,5] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 1
[2,1,3,5,4] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 1
[2,1,4,3,5] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 1
[2,1,4,5,3] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 1
[2,1,5,3,4] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 1
[2,1,5,4,3] => [2,1,5,4,3] => [2,2,1]
=> [2,1]
=> 1
[2,3,4,5,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,3,5,4,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,4,3,5,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,4,5,3,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,5,3,4,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[2,5,4,3,1] => [2,5,4,3,1] => [3,2]
=> [2]
=> 2
[3,2,1,4,5] => [3,2,1,5,4] => [2,2,1]
=> [2,1]
=> 1
[3,2,1,5,4] => [3,2,1,5,4] => [2,2,1]
=> [2,1]
=> 1
Description
The number of positive values of the symmetric group character corresponding to the partition.
For example, the character values of the irreducible representation $S^{(2,2)}$ are $2$ on the conjugacy classes $(4)$ and $(2,2)$, $0$ on the conjugacy classes $(3,1)$ and $(1,1,1,1)$, and $-1$ on the conjugacy class $(2,1,1)$. Therefore, the statistic on the partition $(2,2)$ is $2$.
Matching statistic: St000181
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000181: Posets ⟶ ℤResult quality: 0% ●values known / values provided: 0%●distinct values known / distinct values provided: 8%
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000181: Posets ⟶ ℤResult quality: 0% ●values known / values provided: 0%●distinct values known / distinct values provided: 8%
Values
[1,2,3,4] => [1,4,3,2] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,2,4,3] => [1,4,3,2] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,3,2,4] => [1,4,3,2] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,3,4,2] => [1,4,3,2] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,4,2,3] => [1,4,3,2] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,4,3,2] => [1,4,3,2] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[2,1,3,4] => [2,1,4,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[2,1,4,3] => [2,1,4,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[3,2,1,4] => [3,2,1,4] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ? = 1
[3,4,1,2] => [3,4,1,2] => [4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[4,2,3,1] => [4,2,3,1] => [2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 1
[4,3,2,1] => [4,3,2,1] => [3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,2,3,4,5] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,2,3,5,4] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,2,4,3,5] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,2,4,5,3] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,2,5,3,4] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,2,5,4,3] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,3,2,4,5] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,3,2,5,4] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,3,4,2,5] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,3,4,5,2] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,3,5,2,4] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,3,5,4,2] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,4,2,3,5] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,4,2,5,3] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,4,3,2,5] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,4,3,5,2] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,4,5,2,3] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,4,5,3,2] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,5,2,3,4] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,5,2,4,3] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,5,3,2,4] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,5,3,4,2] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,5,4,2,3] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,5,4,3,2] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[2,1,3,4,5] => [2,1,5,4,3] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
[2,1,3,5,4] => [2,1,5,4,3] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
[2,1,4,3,5] => [2,1,5,4,3] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
[2,1,4,5,3] => [2,1,5,4,3] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
[2,1,5,3,4] => [2,1,5,4,3] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
[2,1,5,4,3] => [2,1,5,4,3] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
[2,3,4,5,1] => [2,5,4,3,1] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[2,3,5,4,1] => [2,5,4,3,1] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[2,4,3,5,1] => [2,5,4,3,1] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[2,4,5,3,1] => [2,5,4,3,1] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[2,5,3,4,1] => [2,5,4,3,1] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[2,5,4,3,1] => [2,5,4,3,1] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[3,2,1,4,5] => [3,2,1,5,4] => [2,1,5,4,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ? = 1
[3,2,1,5,4] => [3,2,1,5,4] => [2,1,5,4,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ? = 1
[3,2,4,5,1] => [3,2,5,4,1] => [2,1,4,3,5] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 1
[3,2,5,4,1] => [3,2,5,4,1] => [2,1,4,3,5] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 1
[3,4,1,2,5] => [3,5,1,4,2] => [5,1,4,2,3] => ([(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
[3,4,1,5,2] => [3,5,1,4,2] => [5,1,4,2,3] => ([(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
[3,4,5,1,2] => [3,5,4,1,2] => [5,1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 2
[3,5,1,2,4] => [3,5,1,4,2] => [5,1,4,2,3] => ([(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
[3,5,1,4,2] => [3,5,1,4,2] => [5,1,4,2,3] => ([(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
[3,5,4,1,2] => [3,5,4,1,2] => [5,1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 2
[4,2,3,1,5] => [4,2,5,1,3] => [2,5,1,3,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? = 1
[4,2,5,1,3] => [4,2,5,1,3] => [2,5,1,3,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? = 1
[4,3,2,1,5] => [4,3,2,1,5] => [3,2,1,5,4] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ? = 1
[4,3,2,5,1] => [4,3,2,5,1] => [3,2,1,4,5] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[4,3,5,1,2] => [4,3,5,1,2] => [5,2,1,3,4] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[4,5,1,2,3] => [4,5,1,3,2] => [5,4,1,2,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[4,5,1,3,2] => [4,5,1,3,2] => [5,4,1,2,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[4,5,2,1,3] => [4,5,2,1,3] => [3,5,1,2,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ? = 2
[4,5,3,1,2] => [4,5,3,1,2] => [5,3,1,2,4] => ([(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
[5,1,2,3,4] => [5,1,4,3,2] => [5,4,3,1,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 2
[5,1,2,4,3] => [5,1,4,3,2] => [5,4,3,1,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 2
[5,1,3,2,4] => [5,1,4,3,2] => [5,4,3,1,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 2
[5,1,3,4,2] => [5,1,4,3,2] => [5,4,3,1,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 2
[5,1,4,2,3] => [5,1,4,3,2] => [5,4,3,1,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 2
[5,1,4,3,2] => [5,1,4,3,2] => [5,4,3,1,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 2
[5,2,1,3,4] => [5,2,1,4,3] => [2,5,4,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? = 1
[5,2,1,4,3] => [5,2,1,4,3] => [2,5,4,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? = 1
[5,2,3,4,1] => [5,2,4,3,1] => [2,4,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 1
[5,2,4,3,1] => [5,2,4,3,1] => [2,4,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 1
[5,3,2,1,4] => [5,3,2,1,4] => [3,2,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ? = 2
[5,3,2,4,1] => [5,3,2,4,1] => [3,2,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 1
[5,3,4,2,1] => [5,3,4,2,1] => [4,2,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 2
Description
The number of connected components of the Hasse diagram for the poset.
Matching statistic: St000635
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000635: Posets ⟶ ℤResult quality: 0% ●values known / values provided: 0%●distinct values known / distinct values provided: 8%
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000635: Posets ⟶ ℤResult quality: 0% ●values known / values provided: 0%●distinct values known / distinct values provided: 8%
Values
[1,2,3,4] => [1,4,3,2] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,2,4,3] => [1,4,3,2] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,3,2,4] => [1,4,3,2] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,3,4,2] => [1,4,3,2] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,4,2,3] => [1,4,3,2] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,4,3,2] => [1,4,3,2] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[2,1,3,4] => [2,1,4,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[2,1,4,3] => [2,1,4,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[3,2,1,4] => [3,2,1,4] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ? = 1
[3,4,1,2] => [3,4,1,2] => [4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[4,2,3,1] => [4,2,3,1] => [2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 1
[4,3,2,1] => [4,3,2,1] => [3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,2,3,4,5] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,2,3,5,4] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,2,4,3,5] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,2,4,5,3] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,2,5,3,4] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,2,5,4,3] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,3,2,4,5] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,3,2,5,4] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,3,4,2,5] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,3,4,5,2] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,3,5,2,4] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,3,5,4,2] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,4,2,3,5] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,4,2,5,3] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,4,3,2,5] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,4,3,5,2] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,4,5,2,3] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,4,5,3,2] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,5,2,3,4] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,5,2,4,3] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,5,3,2,4] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,5,3,4,2] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,5,4,2,3] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,5,4,3,2] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[2,1,3,4,5] => [2,1,5,4,3] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
[2,1,3,5,4] => [2,1,5,4,3] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
[2,1,4,3,5] => [2,1,5,4,3] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
[2,1,4,5,3] => [2,1,5,4,3] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
[2,1,5,3,4] => [2,1,5,4,3] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
[2,1,5,4,3] => [2,1,5,4,3] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
[2,3,4,5,1] => [2,5,4,3,1] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[2,3,5,4,1] => [2,5,4,3,1] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[2,4,3,5,1] => [2,5,4,3,1] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[2,4,5,3,1] => [2,5,4,3,1] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[2,5,3,4,1] => [2,5,4,3,1] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[2,5,4,3,1] => [2,5,4,3,1] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[3,2,1,4,5] => [3,2,1,5,4] => [2,1,5,4,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ? = 1
[3,2,1,5,4] => [3,2,1,5,4] => [2,1,5,4,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ? = 1
[3,2,4,5,1] => [3,2,5,4,1] => [2,1,4,3,5] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 1
[3,2,5,4,1] => [3,2,5,4,1] => [2,1,4,3,5] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 1
[3,4,1,2,5] => [3,5,1,4,2] => [5,1,4,2,3] => ([(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
[3,4,1,5,2] => [3,5,1,4,2] => [5,1,4,2,3] => ([(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
[3,4,5,1,2] => [3,5,4,1,2] => [5,1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 2
[3,5,1,2,4] => [3,5,1,4,2] => [5,1,4,2,3] => ([(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
[3,5,1,4,2] => [3,5,1,4,2] => [5,1,4,2,3] => ([(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
[3,5,4,1,2] => [3,5,4,1,2] => [5,1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 2
[4,2,3,1,5] => [4,2,5,1,3] => [2,5,1,3,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? = 1
[4,2,5,1,3] => [4,2,5,1,3] => [2,5,1,3,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? = 1
[4,3,2,1,5] => [4,3,2,1,5] => [3,2,1,5,4] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ? = 1
[4,3,2,5,1] => [4,3,2,5,1] => [3,2,1,4,5] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[4,3,5,1,2] => [4,3,5,1,2] => [5,2,1,3,4] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[4,5,1,2,3] => [4,5,1,3,2] => [5,4,1,2,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[4,5,1,3,2] => [4,5,1,3,2] => [5,4,1,2,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[4,5,2,1,3] => [4,5,2,1,3] => [3,5,1,2,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ? = 2
[4,5,3,1,2] => [4,5,3,1,2] => [5,3,1,2,4] => ([(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
[5,1,2,3,4] => [5,1,4,3,2] => [5,4,3,1,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 2
[5,1,2,4,3] => [5,1,4,3,2] => [5,4,3,1,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 2
[5,1,3,2,4] => [5,1,4,3,2] => [5,4,3,1,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 2
[5,1,3,4,2] => [5,1,4,3,2] => [5,4,3,1,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 2
[5,1,4,2,3] => [5,1,4,3,2] => [5,4,3,1,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 2
[5,1,4,3,2] => [5,1,4,3,2] => [5,4,3,1,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 2
[5,2,1,3,4] => [5,2,1,4,3] => [2,5,4,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? = 1
[5,2,1,4,3] => [5,2,1,4,3] => [2,5,4,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? = 1
[5,2,3,4,1] => [5,2,4,3,1] => [2,4,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 1
[5,2,4,3,1] => [5,2,4,3,1] => [2,4,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 1
[5,3,2,1,4] => [5,3,2,1,4] => [3,2,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ? = 2
[5,3,2,4,1] => [5,3,2,4,1] => [3,2,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 1
[5,3,4,2,1] => [5,3,4,2,1] => [4,2,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 2
Description
The number of strictly order preserving maps of a poset into itself.
A map $f$ is strictly order preserving if $a < b$ implies $f(a) < f(b)$.
Matching statistic: St001890
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001890: Posets ⟶ ℤResult quality: 0% ●values known / values provided: 0%●distinct values known / distinct values provided: 8%
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001890: Posets ⟶ ℤResult quality: 0% ●values known / values provided: 0%●distinct values known / distinct values provided: 8%
Values
[1,2,3,4] => [1,4,3,2] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,2,4,3] => [1,4,3,2] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,3,2,4] => [1,4,3,2] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,3,4,2] => [1,4,3,2] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,4,2,3] => [1,4,3,2] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,4,3,2] => [1,4,3,2] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 1
[2,1,3,4] => [2,1,4,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[2,1,4,3] => [2,1,4,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[3,2,1,4] => [3,2,1,4] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ? = 1
[3,4,1,2] => [3,4,1,2] => [4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[4,2,3,1] => [4,2,3,1] => [2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
=> ? = 1
[4,3,2,1] => [4,3,2,1] => [3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ? = 2
[1,2,3,4,5] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,2,3,5,4] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,2,4,3,5] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,2,4,5,3] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,2,5,3,4] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,2,5,4,3] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,3,2,4,5] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,3,2,5,4] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,3,4,2,5] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,3,4,5,2] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,3,5,2,4] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,3,5,4,2] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,4,2,3,5] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,4,2,5,3] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,4,3,2,5] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,4,3,5,2] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,4,5,2,3] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,4,5,3,2] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,5,2,3,4] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,5,2,4,3] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,5,3,2,4] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,5,3,4,2] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,5,4,2,3] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,5,4,3,2] => [1,5,4,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[2,1,3,4,5] => [2,1,5,4,3] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
[2,1,3,5,4] => [2,1,5,4,3] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
[2,1,4,3,5] => [2,1,5,4,3] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
[2,1,4,5,3] => [2,1,5,4,3] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
[2,1,5,3,4] => [2,1,5,4,3] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
[2,1,5,4,3] => [2,1,5,4,3] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
[2,3,4,5,1] => [2,5,4,3,1] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[2,3,5,4,1] => [2,5,4,3,1] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[2,4,3,5,1] => [2,5,4,3,1] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[2,4,5,3,1] => [2,5,4,3,1] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[2,5,3,4,1] => [2,5,4,3,1] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[2,5,4,3,1] => [2,5,4,3,1] => [1,4,3,2,5] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[3,2,1,4,5] => [3,2,1,5,4] => [2,1,5,4,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ? = 1
[3,2,1,5,4] => [3,2,1,5,4] => [2,1,5,4,3] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ? = 1
[3,2,4,5,1] => [3,2,5,4,1] => [2,1,4,3,5] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 1
[3,2,5,4,1] => [3,2,5,4,1] => [2,1,4,3,5] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 1
[3,4,1,2,5] => [3,5,1,4,2] => [5,1,4,2,3] => ([(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
[3,4,1,5,2] => [3,5,1,4,2] => [5,1,4,2,3] => ([(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
[3,4,5,1,2] => [3,5,4,1,2] => [5,1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 2
[3,5,1,2,4] => [3,5,1,4,2] => [5,1,4,2,3] => ([(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
[3,5,1,4,2] => [3,5,1,4,2] => [5,1,4,2,3] => ([(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
[3,5,4,1,2] => [3,5,4,1,2] => [5,1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 2
[4,2,3,1,5] => [4,2,5,1,3] => [2,5,1,3,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? = 1
[4,2,5,1,3] => [4,2,5,1,3] => [2,5,1,3,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? = 1
[4,3,2,1,5] => [4,3,2,1,5] => [3,2,1,5,4] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
=> ? = 1
[4,3,2,5,1] => [4,3,2,5,1] => [3,2,1,4,5] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[4,3,5,1,2] => [4,3,5,1,2] => [5,2,1,3,4] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 2
[4,5,1,2,3] => [4,5,1,3,2] => [5,4,1,2,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[4,5,1,3,2] => [4,5,1,3,2] => [5,4,1,2,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 2
[4,5,2,1,3] => [4,5,2,1,3] => [3,5,1,2,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ? = 2
[4,5,3,1,2] => [4,5,3,1,2] => [5,3,1,2,4] => ([(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
[5,1,2,3,4] => [5,1,4,3,2] => [5,4,3,1,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 2
[5,1,2,4,3] => [5,1,4,3,2] => [5,4,3,1,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 2
[5,1,3,2,4] => [5,1,4,3,2] => [5,4,3,1,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 2
[5,1,3,4,2] => [5,1,4,3,2] => [5,4,3,1,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 2
[5,1,4,2,3] => [5,1,4,3,2] => [5,4,3,1,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 2
[5,1,4,3,2] => [5,1,4,3,2] => [5,4,3,1,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 2
[5,2,1,3,4] => [5,2,1,4,3] => [2,5,4,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? = 1
[5,2,1,4,3] => [5,2,1,4,3] => [2,5,4,1,3] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
=> ? = 1
[5,2,3,4,1] => [5,2,4,3,1] => [2,4,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 1
[5,2,4,3,1] => [5,2,4,3,1] => [2,4,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 1
[5,3,2,1,4] => [5,3,2,1,4] => [3,2,5,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
=> ? = 2
[5,3,2,4,1] => [5,3,2,4,1] => [3,2,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 1
[5,3,4,2,1] => [5,3,4,2,1] => [4,2,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
=> ? = 2
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.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!