- FindStat

Your data matches 18 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St000512

Mapping

Mp00163: Signed permutations —permutation⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000512: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

[1,2,3] => [1,2,3] => [1,1,1]
 => [1,1]
 => 0
[1,2,-3] => [1,2,3] => [1,1,1]
 => [1,1]
 => 0
[1,-2,3] => [1,2,3] => [1,1,1]
 => [1,1]
 => 0
[1,-2,-3] => [1,2,3] => [1,1,1]
 => [1,1]
 => 0
[-1,2,3] => [1,2,3] => [1,1,1]
 => [1,1]
 => 0
[-1,2,-3] => [1,2,3] => [1,1,1]
 => [1,1]
 => 0
[-1,-2,3] => [1,2,3] => [1,1,1]
 => [1,1]
 => 0
[-1,-2,-3] => [1,2,3] => [1,1,1]
 => [1,1]
 => 0
[1,2,3,4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 1
[1,2,3,-4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 1
[1,2,-3,4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 1
[1,2,-3,-4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 1
[1,-2,3,4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 1
[1,-2,3,-4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 1
[1,-2,-3,4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 1
[1,-2,-3,-4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 1
[-1,2,3,4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 1
[-1,2,3,-4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 1
[-1,2,-3,4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 1
[-1,2,-3,-4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 1
[-1,-2,3,4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 1
[-1,-2,3,-4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 1
[-1,-2,-3,4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 1
[-1,-2,-3,-4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 1
[1,2,4,3] => [1,2,4,3] => [2,1,1]
 => [1,1]
 => 0
[1,2,4,-3] => [1,2,4,3] => [2,1,1]
 => [1,1]
 => 0
[1,2,-4,3] => [1,2,4,3] => [2,1,1]
 => [1,1]
 => 0
[1,2,-4,-3] => [1,2,4,3] => [2,1,1]
 => [1,1]
 => 0
[1,-2,4,3] => [1,2,4,3] => [2,1,1]
 => [1,1]
 => 0
[1,-2,4,-3] => [1,2,4,3] => [2,1,1]
 => [1,1]
 => 0
[1,-2,-4,3] => [1,2,4,3] => [2,1,1]
 => [1,1]
 => 0
[1,-2,-4,-3] => [1,2,4,3] => [2,1,1]
 => [1,1]
 => 0
[-1,2,4,3] => [1,2,4,3] => [2,1,1]
 => [1,1]
 => 0
[-1,2,4,-3] => [1,2,4,3] => [2,1,1]
 => [1,1]
 => 0
[-1,2,-4,3] => [1,2,4,3] => [2,1,1]
 => [1,1]
 => 0
[-1,2,-4,-3] => [1,2,4,3] => [2,1,1]
 => [1,1]
 => 0
[-1,-2,4,3] => [1,2,4,3] => [2,1,1]
 => [1,1]
 => 0
[-1,-2,4,-3] => [1,2,4,3] => [2,1,1]
 => [1,1]
 => 0
[-1,-2,-4,3] => [1,2,4,3] => [2,1,1]
 => [1,1]
 => 0
[-1,-2,-4,-3] => [1,2,4,3] => [2,1,1]
 => [1,1]
 => 0
[1,3,2,4] => [1,3,2,4] => [2,1,1]
 => [1,1]
 => 0
[1,3,2,-4] => [1,3,2,4] => [2,1,1]
 => [1,1]
 => 0
[1,3,-2,4] => [1,3,2,4] => [2,1,1]
 => [1,1]
 => 0
[1,3,-2,-4] => [1,3,2,4] => [2,1,1]
 => [1,1]
 => 0
[1,-3,2,4] => [1,3,2,4] => [2,1,1]
 => [1,1]
 => 0
[1,-3,2,-4] => [1,3,2,4] => [2,1,1]
 => [1,1]
 => 0
[1,-3,-2,4] => [1,3,2,4] => [2,1,1]
 => [1,1]
 => 0
[1,-3,-2,-4] => [1,3,2,4] => [2,1,1]
 => [1,1]
 => 0
[-1,3,2,4] => [1,3,2,4] => [2,1,1]
 => [1,1]
 => 0
[-1,3,2,-4] => [1,3,2,4] => [2,1,1]
 => [1,1]
 => 0

Description

The number of invariant subsets of size 3 when acting with a permutation of given cycle type.

Matching statistic: St001624
(load all 3 compositions to match this statistic)

Mapping

Mp00163: Signed permutations —permutation⟶ Permutations
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
St001624: Lattices ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 14%

Values

[1,2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,-2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,-2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-1,2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-1,2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-1,-2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-1,-2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,-2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,-2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,-2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,-2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,-2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,-2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,-2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,-2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,-2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,-2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,-2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,-2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,-2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,-2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,-2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,-2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,-3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,-3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,-3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,-3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,-3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,-3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,-3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,-3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,3,4,2] => [1,3,4,2] => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ? = 0 + 2
[1,3,4,-2] => [1,3,4,2] => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ? = 0 + 2
[2,5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,2,1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,2,1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,2,-1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,2,-1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,-2,1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,-2,1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,-2,-1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,-2,-1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,-5,2,1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,-5,2,1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2

Description

The breadth of a lattice. The '''breadth''' of a lattice is the least integer

$b$ such that any join

$x_1\vee x_2\vee\cdots\vee x_n$ , with

$n > b$ , can be expressed as a join over a proper subset of

$\{x_1,x_2,\ldots,x_n\}$ .

Matching statistic: St001630
(load all 3 compositions to match this statistic)

Mapping

Mp00163: Signed permutations —permutation⟶ Permutations
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
St001630: Lattices ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 14%

Values

[1,2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,-2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,-2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-1,2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-1,2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-1,-2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-1,-2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,-2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,-2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,-2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,-2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,-2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,-2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,-2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,-2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,-2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,-2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,-2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,-2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,-2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,-2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,-2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,-2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,-3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,-3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,-3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,-3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,-3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,-3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,-3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,-3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,3,4,2] => [1,3,4,2] => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ? = 0 + 2
[1,3,4,-2] => [1,3,4,2] => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ? = 0 + 2
[2,5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,2,1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,2,1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,2,-1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,2,-1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,-2,1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,-2,1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,-2,-1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,-2,-1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,-5,2,1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,-5,2,1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2

Description

The global dimension of the incidence algebra of the lattice over the rational numbers.

Matching statistic: St001878
(load all 3 compositions to match this statistic)

Mapping

Mp00163: Signed permutations —permutation⟶ Permutations
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
St001878: Lattices ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 14%

Values

[1,2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,-2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,-2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-1,2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-1,2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-1,-2,3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-1,-2,-3] => [1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,-2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,-2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,-2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,-2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,-2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,-2,3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,-2,-3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,-2,-3,-4] => [1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,-2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,-2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,-2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,-2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,-2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,-2,4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,-2,-4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,-2,-4,-3] => [1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,-3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,-3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,-3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,-3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,-3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,-3,2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,-3,-2,4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,-3,-2,-4] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,3,4,2] => [1,3,4,2] => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ? = 0 + 2
[1,3,4,-2] => [1,3,4,2] => [1,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => ? = 0 + 2
[2,5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[2,-5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,-1,4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,-1,4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,-1,-4,3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[-2,-5,-1,-4,-3] => [2,5,1,4,3] => [4,2,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,2,1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,2,1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,2,-1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,2,-1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,-2,1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,-2,1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,-2,-1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,5,-2,-1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,-5,2,1,4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[3,-5,2,1,-4] => [3,5,2,1,4] => [2,5,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2

Description

The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.

Matching statistic: St001491

Mapping

Mp00163: Signed permutations —permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St001491: Binary words ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 14%

Values

[1,2,3] => [1,2,3] => [3]
 => 1000 => 1 = 0 + 1
[1,2,-3] => [1,2,3] => [3]
 => 1000 => 1 = 0 + 1
[1,-2,3] => [1,2,3] => [3]
 => 1000 => 1 = 0 + 1
[1,-2,-3] => [1,2,3] => [3]
 => 1000 => 1 = 0 + 1
[-1,2,3] => [1,2,3] => [3]
 => 1000 => 1 = 0 + 1
[-1,2,-3] => [1,2,3] => [3]
 => 1000 => 1 = 0 + 1
[-1,-2,3] => [1,2,3] => [3]
 => 1000 => 1 = 0 + 1
[-1,-2,-3] => [1,2,3] => [3]
 => 1000 => 1 = 0 + 1
[1,2,3,4] => [1,2,3,4] => [4]
 => 10000 => ? = 1 + 1
[1,2,3,-4] => [1,2,3,4] => [4]
 => 10000 => ? = 1 + 1
[1,2,-3,4] => [1,2,3,4] => [4]
 => 10000 => ? = 1 + 1
[1,2,-3,-4] => [1,2,3,4] => [4]
 => 10000 => ? = 1 + 1
[1,-2,3,4] => [1,2,3,4] => [4]
 => 10000 => ? = 1 + 1
[1,-2,3,-4] => [1,2,3,4] => [4]
 => 10000 => ? = 1 + 1
[1,-2,-3,4] => [1,2,3,4] => [4]
 => 10000 => ? = 1 + 1
[1,-2,-3,-4] => [1,2,3,4] => [4]
 => 10000 => ? = 1 + 1
[-1,2,3,4] => [1,2,3,4] => [4]
 => 10000 => ? = 1 + 1
[-1,2,3,-4] => [1,2,3,4] => [4]
 => 10000 => ? = 1 + 1
[-1,2,-3,4] => [1,2,3,4] => [4]
 => 10000 => ? = 1 + 1
[-1,2,-3,-4] => [1,2,3,4] => [4]
 => 10000 => ? = 1 + 1
[-1,-2,3,4] => [1,2,3,4] => [4]
 => 10000 => ? = 1 + 1
[-1,-2,3,-4] => [1,2,3,4] => [4]
 => 10000 => ? = 1 + 1
[-1,-2,-3,4] => [1,2,3,4] => [4]
 => 10000 => ? = 1 + 1
[-1,-2,-3,-4] => [1,2,3,4] => [4]
 => 10000 => ? = 1 + 1
[1,2,4,3] => [1,2,4,3] => [3,1]
 => 10010 => ? = 0 + 1
[1,2,4,-3] => [1,2,4,3] => [3,1]
 => 10010 => ? = 0 + 1
[1,2,-4,3] => [1,2,4,3] => [3,1]
 => 10010 => ? = 0 + 1
[1,2,-4,-3] => [1,2,4,3] => [3,1]
 => 10010 => ? = 0 + 1
[1,-2,4,3] => [1,2,4,3] => [3,1]
 => 10010 => ? = 0 + 1
[1,-2,4,-3] => [1,2,4,3] => [3,1]
 => 10010 => ? = 0 + 1
[1,-2,-4,3] => [1,2,4,3] => [3,1]
 => 10010 => ? = 0 + 1
[1,-2,-4,-3] => [1,2,4,3] => [3,1]
 => 10010 => ? = 0 + 1
[-1,2,4,3] => [1,2,4,3] => [3,1]
 => 10010 => ? = 0 + 1
[-1,2,4,-3] => [1,2,4,3] => [3,1]
 => 10010 => ? = 0 + 1
[-1,2,-4,3] => [1,2,4,3] => [3,1]
 => 10010 => ? = 0 + 1
[-1,2,-4,-3] => [1,2,4,3] => [3,1]
 => 10010 => ? = 0 + 1
[-1,-2,4,3] => [1,2,4,3] => [3,1]
 => 10010 => ? = 0 + 1
[-1,-2,4,-3] => [1,2,4,3] => [3,1]
 => 10010 => ? = 0 + 1
[-1,-2,-4,3] => [1,2,4,3] => [3,1]
 => 10010 => ? = 0 + 1
[-1,-2,-4,-3] => [1,2,4,3] => [3,1]
 => 10010 => ? = 0 + 1
[1,3,2,4] => [1,3,2,4] => [3,1]
 => 10010 => ? = 0 + 1
[1,3,2,-4] => [1,3,2,4] => [3,1]
 => 10010 => ? = 0 + 1
[1,3,-2,4] => [1,3,2,4] => [3,1]
 => 10010 => ? = 0 + 1
[1,3,-2,-4] => [1,3,2,4] => [3,1]
 => 10010 => ? = 0 + 1
[1,-3,2,4] => [1,3,2,4] => [3,1]
 => 10010 => ? = 0 + 1
[1,-3,2,-4] => [1,3,2,4] => [3,1]
 => 10010 => ? = 0 + 1
[1,-3,-2,4] => [1,3,2,4] => [3,1]
 => 10010 => ? = 0 + 1
[1,-3,-2,-4] => [1,3,2,4] => [3,1]
 => 10010 => ? = 0 + 1
[-1,3,2,4] => [1,3,2,4] => [3,1]
 => 10010 => ? = 0 + 1
[-1,3,2,-4] => [1,3,2,4] => [3,1]
 => 10010 => ? = 0 + 1
[-1,3,-2,4] => [1,3,2,4] => [3,1]
 => 10010 => ? = 0 + 1
[-1,3,-2,-4] => [1,3,2,4] => [3,1]
 => 10010 => ? = 0 + 1
[-1,-3,2,4] => [1,3,2,4] => [3,1]
 => 10010 => ? = 0 + 1
[-1,-3,2,-4] => [1,3,2,4] => [3,1]
 => 10010 => ? = 0 + 1
[-1,-3,-2,4] => [1,3,2,4] => [3,1]
 => 10010 => ? = 0 + 1
[-1,-3,-2,-4] => [1,3,2,4] => [3,1]
 => 10010 => ? = 0 + 1
[1,3,4,2] => [1,3,4,2] => [3,1]
 => 10010 => ? = 0 + 1
[1,3,4,-2] => [1,3,4,2] => [3,1]
 => 10010 => ? = 0 + 1
[2,1,4,3] => [2,1,4,3] => [2,2]
 => 1100 => 1 = 0 + 1
[2,1,4,-3] => [2,1,4,3] => [2,2]
 => 1100 => 1 = 0 + 1
[2,1,-4,3] => [2,1,4,3] => [2,2]
 => 1100 => 1 = 0 + 1
[2,1,-4,-3] => [2,1,4,3] => [2,2]
 => 1100 => 1 = 0 + 1
[2,-1,4,3] => [2,1,4,3] => [2,2]
 => 1100 => 1 = 0 + 1
[2,-1,4,-3] => [2,1,4,3] => [2,2]
 => 1100 => 1 = 0 + 1
[2,-1,-4,3] => [2,1,4,3] => [2,2]
 => 1100 => 1 = 0 + 1
[2,-1,-4,-3] => [2,1,4,3] => [2,2]
 => 1100 => 1 = 0 + 1
[-2,1,4,3] => [2,1,4,3] => [2,2]
 => 1100 => 1 = 0 + 1
[-2,1,4,-3] => [2,1,4,3] => [2,2]
 => 1100 => 1 = 0 + 1
[-2,1,-4,3] => [2,1,4,3] => [2,2]
 => 1100 => 1 = 0 + 1
[-2,1,-4,-3] => [2,1,4,3] => [2,2]
 => 1100 => 1 = 0 + 1
[-2,-1,4,3] => [2,1,4,3] => [2,2]
 => 1100 => 1 = 0 + 1
[-2,-1,4,-3] => [2,1,4,3] => [2,2]
 => 1100 => 1 = 0 + 1
[-2,-1,-4,3] => [2,1,4,3] => [2,2]
 => 1100 => 1 = 0 + 1
[-2,-1,-4,-3] => [2,1,4,3] => [2,2]
 => 1100 => 1 = 0 + 1
[2,4,1,3] => [2,4,1,3] => [2,2]
 => 1100 => 1 = 0 + 1
[2,4,1,-3] => [2,4,1,3] => [2,2]
 => 1100 => 1 = 0 + 1
[2,4,-1,3] => [2,4,1,3] => [2,2]
 => 1100 => 1 = 0 + 1
[2,4,-1,-3] => [2,4,1,3] => [2,2]
 => 1100 => 1 = 0 + 1
[2,-4,1,3] => [2,4,1,3] => [2,2]
 => 1100 => 1 = 0 + 1
[2,-4,1,-3] => [2,4,1,3] => [2,2]
 => 1100 => 1 = 0 + 1
[2,-4,-1,3] => [2,4,1,3] => [2,2]
 => 1100 => 1 = 0 + 1
[2,-4,-1,-3] => [2,4,1,3] => [2,2]
 => 1100 => 1 = 0 + 1
[-2,4,1,3] => [2,4,1,3] => [2,2]
 => 1100 => 1 = 0 + 1
[-2,4,1,-3] => [2,4,1,3] => [2,2]
 => 1100 => 1 = 0 + 1
[-2,4,-1,3] => [2,4,1,3] => [2,2]
 => 1100 => 1 = 0 + 1
[-2,4,-1,-3] => [2,4,1,3] => [2,2]
 => 1100 => 1 = 0 + 1
[-2,-4,1,3] => [2,4,1,3] => [2,2]
 => 1100 => 1 = 0 + 1
[-2,-4,1,-3] => [2,4,1,3] => [2,2]
 => 1100 => 1 = 0 + 1
[-2,-4,-1,3] => [2,4,1,3] => [2,2]
 => 1100 => 1 = 0 + 1
[-2,-4,-1,-3] => [2,4,1,3] => [2,2]
 => 1100 => 1 = 0 + 1
[3,1,4,2] => [3,1,4,2] => [2,2]
 => 1100 => 1 = 0 + 1
[3,1,4,-2] => [3,1,4,2] => [2,2]
 => 1100 => 1 = 0 + 1
[3,1,-4,2] => [3,1,4,2] => [2,2]
 => 1100 => 1 = 0 + 1
[3,1,-4,-2] => [3,1,4,2] => [2,2]
 => 1100 => 1 = 0 + 1
[3,-1,4,2] => [3,1,4,2] => [2,2]
 => 1100 => 1 = 0 + 1
[3,-1,4,-2] => [3,1,4,2] => [2,2]
 => 1100 => 1 = 0 + 1
[3,-1,-4,2] => [3,1,4,2] => [2,2]
 => 1100 => 1 = 0 + 1
[3,-1,-4,-2] => [3,1,4,2] => [2,2]
 => 1100 => 1 = 0 + 1
[-3,1,4,2] => [3,1,4,2] => [2,2]
 => 1100 => 1 = 0 + 1
[-3,1,4,-2] => [3,1,4,2] => [2,2]
 => 1100 => 1 = 0 + 1

Description

The number of indecomposable projective-injective modules in the algebra corresponding to a subset. Let

$A_n=K[x]/(x^n)$ . We associate to a nonempty subset S of an (n-1)-set the module

$M_S$ , which is the direct sum of

$A_n$ -modules with indecomposable non-projective direct summands of dimension

$i$ when

$i$ is in

$S$ (note that such modules have vector space dimension at most n-1). Then the corresponding algebra associated to S is the stable endomorphism ring of

$M_S$ . We decode the subset as a binary word so that for example the subset

$S=\{1,3 \}$ of

$\{1,2,3 \}$ is decoded as 101.

Matching statistic: St001754
(load all 5 compositions to match this statistic)

Mapping

Mp00163: Signed permutations —permutation⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
St001754: Lattices ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 14%

Values

[1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 2
[1,2,-3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 2
[1,-2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 2
[1,-2,-3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 2
[-1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 2
[-1,2,-3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 2
[-1,-2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 2
[-1,-2,-3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 2
[1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,2,3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,2,-3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,2,-3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,-2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,-2,3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,-2,-3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,-2,-3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,2,3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,2,-3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,2,-3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,-2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,-2,3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,-2,-3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,-2,-3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,2,4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,2,-4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,2,-4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,-2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,-2,4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,-2,-4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,-2,-4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,2,4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,2,-4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,2,-4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,-2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,-2,4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,-2,-4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,-2,-4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,-3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,-3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,-3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,-3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[2,4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[2,4,1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[2,4,-1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[2,4,-1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[2,-4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[2,-4,1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[2,-4,-1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[2,-4,-1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-2,4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-2,4,1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-2,4,-1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-2,4,-1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-2,-4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-2,-4,1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-2,-4,-1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-2,-4,-1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[3,1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[3,1,4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[3,1,-4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[3,1,-4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[3,-1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[3,-1,4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[3,-1,-4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[3,-1,-4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-3,1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-3,1,4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-3,1,-4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-3,1,-4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-3,-1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-3,-1,4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-3,-1,-4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-3,-1,-4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2

Description

The number of tolerances of a finite lattice. Let

$L$ be a lattice. A tolerance

$\tau$ is a reflexive and symmetric relation on

$L$ which is compatible with meet and join. Equivalently, a tolerance of

$L$ is the image of a congruence by a surjective lattice homomorphism onto

$L$ . The number of tolerances of a chain of

$n$ elements is the Catalan number

$\frac{1}{n+1}\binom{2n}{n}$ , see [2].

Matching statistic: St001880

Mapping

Mp00161: Signed permutations —reverse⟶ Signed permutations
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 14%

Values

[1,2,3] => [3,2,1] => [3,2,1] => ([],3)
 => ? = 0 + 1
[1,2,-3] => [-3,2,1] => [3,2,1] => ([],3)
 => ? = 0 + 1
[1,-2,3] => [3,-2,1] => [3,2,1] => ([],3)
 => ? = 0 + 1
[1,-2,-3] => [-3,-2,1] => [3,2,1] => ([],3)
 => ? = 0 + 1
[-1,2,3] => [3,2,-1] => [3,2,1] => ([],3)
 => ? = 0 + 1
[-1,2,-3] => [-3,2,-1] => [3,2,1] => ([],3)
 => ? = 0 + 1
[-1,-2,3] => [3,-2,-1] => [3,2,1] => ([],3)
 => ? = 0 + 1
[-1,-2,-3] => [-3,-2,-1] => [3,2,1] => ([],3)
 => ? = 0 + 1
[1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ([],4)
 => ? = 1 + 1
[1,2,3,-4] => [-4,3,2,1] => [4,3,2,1] => ([],4)
 => ? = 1 + 1
[1,2,-3,4] => [4,-3,2,1] => [4,3,2,1] => ([],4)
 => ? = 1 + 1
[1,2,-3,-4] => [-4,-3,2,1] => [4,3,2,1] => ([],4)
 => ? = 1 + 1
[1,-2,3,4] => [4,3,-2,1] => [4,3,2,1] => ([],4)
 => ? = 1 + 1
[1,-2,3,-4] => [-4,3,-2,1] => [4,3,2,1] => ([],4)
 => ? = 1 + 1
[1,-2,-3,4] => [4,-3,-2,1] => [4,3,2,1] => ([],4)
 => ? = 1 + 1
[1,-2,-3,-4] => [-4,-3,-2,1] => [4,3,2,1] => ([],4)
 => ? = 1 + 1
[-1,2,3,4] => [4,3,2,-1] => [4,3,2,1] => ([],4)
 => ? = 1 + 1
[-1,2,3,-4] => [-4,3,2,-1] => [4,3,2,1] => ([],4)
 => ? = 1 + 1
[-1,2,-3,4] => [4,-3,2,-1] => [4,3,2,1] => ([],4)
 => ? = 1 + 1
[-1,2,-3,-4] => [-4,-3,2,-1] => [4,3,2,1] => ([],4)
 => ? = 1 + 1
[-1,-2,3,4] => [4,3,-2,-1] => [4,3,2,1] => ([],4)
 => ? = 1 + 1
[-1,-2,3,-4] => [-4,3,-2,-1] => [4,3,2,1] => ([],4)
 => ? = 1 + 1
[-1,-2,-3,4] => [4,-3,-2,-1] => [4,3,2,1] => ([],4)
 => ? = 1 + 1
[-1,-2,-3,-4] => [-4,-3,-2,-1] => [4,3,2,1] => ([],4)
 => ? = 1 + 1
[1,2,4,3] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
 => ? = 0 + 1
[1,2,4,-3] => [-3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
 => ? = 0 + 1
[1,2,-4,3] => [3,-4,2,1] => [3,4,2,1] => ([(2,3)],4)
 => ? = 0 + 1
[1,2,-4,-3] => [-3,-4,2,1] => [3,4,2,1] => ([(2,3)],4)
 => ? = 0 + 1
[1,-2,4,3] => [3,4,-2,1] => [3,4,2,1] => ([(2,3)],4)
 => ? = 0 + 1
[1,-2,4,-3] => [-3,4,-2,1] => [3,4,2,1] => ([(2,3)],4)
 => ? = 0 + 1
[1,-2,-4,3] => [3,-4,-2,1] => [3,4,2,1] => ([(2,3)],4)
 => ? = 0 + 1
[1,-2,-4,-3] => [-3,-4,-2,1] => [3,4,2,1] => ([(2,3)],4)
 => ? = 0 + 1
[-1,2,4,3] => [3,4,2,-1] => [3,4,2,1] => ([(2,3)],4)
 => ? = 0 + 1
[-1,2,4,-3] => [-3,4,2,-1] => [3,4,2,1] => ([(2,3)],4)
 => ? = 0 + 1
[-1,2,-4,3] => [3,-4,2,-1] => [3,4,2,1] => ([(2,3)],4)
 => ? = 0 + 1
[-1,2,-4,-3] => [-3,-4,2,-1] => [3,4,2,1] => ([(2,3)],4)
 => ? = 0 + 1
[-1,-2,4,3] => [3,4,-2,-1] => [3,4,2,1] => ([(2,3)],4)
 => ? = 0 + 1
[-1,-2,4,-3] => [-3,4,-2,-1] => [3,4,2,1] => ([(2,3)],4)
 => ? = 0 + 1
[-1,-2,-4,3] => [3,-4,-2,-1] => [3,4,2,1] => ([(2,3)],4)
 => ? = 0 + 1
[-1,-2,-4,-3] => [-3,-4,-2,-1] => [3,4,2,1] => ([(2,3)],4)
 => ? = 0 + 1
[1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ([(2,3)],4)
 => ? = 0 + 1
[1,3,2,-4] => [-4,2,3,1] => [4,2,3,1] => ([(2,3)],4)
 => ? = 0 + 1
[1,3,-2,4] => [4,-2,3,1] => [4,2,3,1] => ([(2,3)],4)
 => ? = 0 + 1
[1,3,-2,-4] => [-4,-2,3,1] => [4,2,3,1] => ([(2,3)],4)
 => ? = 0 + 1
[1,-3,2,4] => [4,2,-3,1] => [4,2,3,1] => ([(2,3)],4)
 => ? = 0 + 1
[1,-3,2,-4] => [-4,2,-3,1] => [4,2,3,1] => ([(2,3)],4)
 => ? = 0 + 1
[1,-3,-2,4] => [4,-2,-3,1] => [4,2,3,1] => ([(2,3)],4)
 => ? = 0 + 1
[1,-3,-2,-4] => [-4,-2,-3,1] => [4,2,3,1] => ([(2,3)],4)
 => ? = 0 + 1
[-1,3,2,4] => [4,2,3,-1] => [4,2,3,1] => ([(2,3)],4)
 => ? = 0 + 1
[-1,3,2,-4] => [-4,2,3,-1] => [4,2,3,1] => ([(2,3)],4)
 => ? = 0 + 1
[5,2,3,4,1] => [1,4,3,2,5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[5,2,3,4,-1] => [-1,4,3,2,5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[5,2,3,-4,1] => [1,-4,3,2,5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[5,2,3,-4,-1] => [-1,-4,3,2,5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[5,2,-3,4,1] => [1,4,-3,2,5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[5,2,-3,4,-1] => [-1,4,-3,2,5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[5,2,-3,-4,1] => [1,-4,-3,2,5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[5,2,-3,-4,-1] => [-1,-4,-3,2,5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[5,-2,3,4,1] => [1,4,3,-2,5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[5,-2,3,4,-1] => [-1,4,3,-2,5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[5,-2,3,-4,1] => [1,-4,3,-2,5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[5,-2,3,-4,-1] => [-1,-4,3,-2,5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[5,-2,-3,4,1] => [1,4,-3,-2,5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[5,-2,-3,4,-1] => [-1,4,-3,-2,5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[5,-2,-3,-4,1] => [1,-4,-3,-2,5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[5,-2,-3,-4,-1] => [-1,-4,-3,-2,5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[-5,2,3,4,1] => [1,4,3,2,-5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[-5,2,3,4,-1] => [-1,4,3,2,-5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[-5,2,3,-4,1] => [1,-4,3,2,-5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[-5,2,3,-4,-1] => [-1,-4,3,2,-5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[-5,2,-3,4,1] => [1,4,-3,2,-5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[-5,2,-3,4,-1] => [-1,4,-3,2,-5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[-5,2,-3,-4,1] => [1,-4,-3,2,-5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[-5,2,-3,-4,-1] => [-1,-4,-3,2,-5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[-5,-2,3,4,1] => [1,4,3,-2,-5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[-5,-2,3,4,-1] => [-1,4,3,-2,-5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[-5,-2,3,-4,1] => [1,-4,3,-2,-5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[-5,-2,3,-4,-1] => [-1,-4,3,-2,-5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[-5,-2,-3,4,1] => [1,4,-3,-2,-5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[-5,-2,-3,4,-1] => [-1,4,-3,-2,-5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[-5,-2,-3,-4,1] => [1,-4,-3,-2,-5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1
[-5,-2,-3,-4,-1] => [-1,-4,-3,-2,-5] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1 = 0 + 1

Description

The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.

Matching statistic: St000080

Mapping

Mp00163: Signed permutations —permutation⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St000080: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 14%

Values

[1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 2
[1,2,-3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 2
[1,-2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 2
[1,-2,-3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 2
[-1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 2
[-1,2,-3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 2
[-1,-2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 2
[-1,-2,-3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 2
[1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,2,3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,2,-3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,2,-3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,-2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,-2,3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,-2,-3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,-2,-3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,2,3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,2,-3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,2,-3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,-2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,-2,3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,-2,-3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[-1,-2,-3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 2
[1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,2,4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,2,-4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,2,-4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,-2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,-2,4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,-2,-4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,-2,-4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,2,4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,2,-4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,2,-4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,-2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,-2,4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,-2,-4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[-1,-2,-4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 2
[1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,-3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,-3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,-3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[1,-3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[-1,3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 2
[2,4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[2,4,1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[2,4,-1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[2,4,-1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[2,-4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[2,-4,1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[2,-4,-1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[2,-4,-1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-2,4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-2,4,1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-2,4,-1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-2,4,-1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-2,-4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-2,-4,1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-2,-4,-1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-2,-4,-1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[3,1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[3,1,4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[3,1,-4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[3,1,-4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[3,-1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[3,-1,4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[3,-1,-4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[3,-1,-4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-3,1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-3,1,4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-3,1,-4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-3,1,-4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-3,-1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-3,-1,4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-3,-1,-4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[-3,-1,-4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2

Description

The rank of the poset.

Matching statistic: St000189

Mapping

Mp00163: Signed permutations —permutation⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St000189: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 14%

Values

[1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 6
[1,2,-3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 6
[1,-2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 6
[1,-2,-3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 6
[-1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 6
[-1,2,-3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 6
[-1,-2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 6
[-1,-2,-3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 6
[1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 6
[1,2,3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 6
[1,2,-3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 6
[1,2,-3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 6
[1,-2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 6
[1,-2,3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 6
[1,-2,-3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 6
[1,-2,-3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 6
[-1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 6
[-1,2,3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 6
[-1,2,-3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 6
[-1,2,-3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 6
[-1,-2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 6
[-1,-2,3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 6
[-1,-2,-3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 6
[-1,-2,-3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 6
[1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 6
[1,2,4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 6
[1,2,-4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 6
[1,2,-4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 6
[1,-2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 6
[1,-2,4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 6
[1,-2,-4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 6
[1,-2,-4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 6
[-1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 6
[-1,2,4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 6
[-1,2,-4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 6
[-1,2,-4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 6
[-1,-2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 6
[-1,-2,4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 6
[-1,-2,-4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 6
[-1,-2,-4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 6
[1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 6
[1,3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 6
[1,3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 6
[1,3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 6
[1,-3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 6
[1,-3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 6
[1,-3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 6
[1,-3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 6
[-1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 6
[-1,3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 6
[2,4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[2,4,1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[2,4,-1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[2,4,-1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[2,-4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[2,-4,1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[2,-4,-1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[2,-4,-1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[-2,4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[-2,4,1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[-2,4,-1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[-2,4,-1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[-2,-4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[-2,-4,1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[-2,-4,-1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[-2,-4,-1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[3,1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[3,1,4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[3,1,-4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[3,1,-4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[3,-1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[3,-1,4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[3,-1,-4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[3,-1,-4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[-3,1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[-3,1,4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[-3,1,-4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[-3,1,-4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[-3,-1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[-3,-1,4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[-3,-1,-4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6
[-3,-1,-4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 6 = 0 + 6

Description

The number of elements in the poset.

Matching statistic: St000307

Mapping

Mp00163: Signed permutations —permutation⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St000307: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 14%

Values

[1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 8
[1,2,-3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 8
[1,-2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 8
[1,-2,-3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 8
[-1,2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 8
[-1,2,-3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 8
[-1,-2,3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 8
[-1,-2,-3] => [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 0 + 8
[1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 8
[1,2,3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 8
[1,2,-3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 8
[1,2,-3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 8
[1,-2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 8
[1,-2,3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 8
[1,-2,-3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 8
[1,-2,-3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 8
[-1,2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 8
[-1,2,3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 8
[-1,2,-3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 8
[-1,2,-3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 8
[-1,-2,3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 8
[-1,-2,3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 8
[-1,-2,-3,4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 8
[-1,-2,-3,-4] => [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
 => ? = 1 + 8
[1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 8
[1,2,4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 8
[1,2,-4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 8
[1,2,-4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 8
[1,-2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 8
[1,-2,4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 8
[1,-2,-4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 8
[1,-2,-4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 8
[-1,2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 8
[-1,2,4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 8
[-1,2,-4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 8
[-1,2,-4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 8
[-1,-2,4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 8
[-1,-2,4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 8
[-1,-2,-4,3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 8
[-1,-2,-4,-3] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ? = 0 + 8
[1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 8
[1,3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 8
[1,3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 8
[1,3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 8
[1,-3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 8
[1,-3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 8
[1,-3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 8
[1,-3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 8
[-1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 8
[-1,3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 0 + 8
[2,4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[2,4,1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[2,4,-1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[2,4,-1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[2,-4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[2,-4,1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[2,-4,-1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[2,-4,-1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[-2,4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[-2,4,1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[-2,4,-1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[-2,4,-1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[-2,-4,1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[-2,-4,1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[-2,-4,-1,3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[-2,-4,-1,-3] => [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[3,1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[3,1,4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[3,1,-4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[3,1,-4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[3,-1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[3,-1,4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[3,-1,-4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[3,-1,-4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[-3,1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[-3,1,4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[-3,1,-4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[-3,1,-4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[-3,-1,4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[-3,-1,4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[-3,-1,-4,2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8
[-3,-1,-4,-2] => [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => 8 = 0 + 8

Description

The number of rowmotion orbits of a poset. Rowmotion is an operation on order ideals in a poset

$P$ . It sends an order ideal

$I$ to the order ideal generated by the minimal antichain of

$P \setminus I$ .

The following 8 statistics, ordered by result quality, also match your data. Click on any of them to see the details.

St001879The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice. St000104The number of facets in the order polytope of this poset. St000151The number of facets in the chain polytope of the poset. St000180The number of chains of a poset. St000100The number of linear extensions of a poset. St001909The number of interval-closed sets of a poset. St000634The number of endomorphisms of a poset. St001645The pebbling number of a connected graph.