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Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000656
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St000656: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St000656: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[-1,-2] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> 2
[2,-1] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> 2
[-2,1] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> 2
[1,-2,-3] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> 2
[-1,2,-3] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> 2
[-1,-2,3] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> 2
[-1,-2,-3] => [1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 3
[1,3,-2] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> 2
[1,-3,2] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> 2
[-1,3,-2] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> 4
[-1,-3,2] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> 4
[2,-1,3] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> 2
[2,-1,-3] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> 4
[-2,1,3] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> 2
[-2,1,-3] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> 4
[2,3,-1] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[2,-3,1] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-2,3,1] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-2,-3,-1] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[3,1,-2] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[3,-1,2] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-3,1,2] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-3,-1,-2] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[3,2,-1] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> 2
[3,-2,-1] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> 4
[-3,2,1] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> 2
[-3,-2,1] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> 4
[1,2,-3,-4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> 2
[1,-2,3,-4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> 2
[1,-2,-3,4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> 2
[1,-2,-3,-4] => [1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-1,2,3,-4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> 2
[-1,2,-3,4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> 2
[-1,2,-3,-4] => [1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-1,-2,3,4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> 2
[-1,-2,3,-4] => [1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-1,-2,-3,4] => [1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-1,-2,-3,-4] => [1,1,1,1]
=> [[1,1,1,1],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,2,4,-3] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> 2
[1,2,-4,3] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> 2
[1,-2,4,-3] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> 4
[1,-2,-4,3] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> 4
[-1,2,4,-3] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> 4
[-1,2,-4,3] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> 4
[-1,-2,4,3] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> 2
[-1,-2,4,-3] => [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> 5
[-1,-2,-4,3] => [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> 5
[-1,-2,-4,-3] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> 2
[1,3,-2,4] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> 2
[1,3,-2,-4] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> 4
Description
The number of cuts of a poset.
A cut is a subset $A$ of the poset such that the set of lower bounds of the set of upper bounds of $A$ is exactly $A$.
Matching statistic: St001880
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 46% ●values known / values provided: 46%●distinct values known / distinct values provided: 67%
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 46% ●values known / values provided: 46%●distinct values known / distinct values provided: 67%
Values
[-1,-2] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2
[2,-1] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2
[-2,1] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2
[1,-2,-3] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2
[-1,2,-3] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2
[-1,-2,3] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2
[-1,-2,-3] => [1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 3
[1,3,-2] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2
[1,-3,2] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2
[-1,3,-2] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 4
[-1,-3,2] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 4
[2,-1,3] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2
[2,-1,-3] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 4
[-2,1,3] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2
[-2,1,-3] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 4
[2,3,-1] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[2,-3,1] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-2,3,1] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-2,-3,-1] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[3,1,-2] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[3,-1,2] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-3,1,2] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-3,-1,-2] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[3,2,-1] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2
[3,-2,-1] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 4
[-3,2,1] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2
[-3,-2,1] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 4
[1,2,-3,-4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2
[1,-2,3,-4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2
[1,-2,-3,4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2
[1,-2,-3,-4] => [1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-1,2,3,-4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2
[-1,2,-3,4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2
[-1,2,-3,-4] => [1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-1,-2,3,4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2
[-1,-2,3,-4] => [1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-1,-2,-3,4] => [1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-1,-2,-3,-4] => [1,1,1,1]
=> [[1,1,1,1],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,2,4,-3] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2
[1,2,-4,3] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2
[1,-2,4,-3] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 4
[1,-2,-4,3] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 4
[-1,2,4,-3] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 4
[-1,2,-4,3] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 4
[-1,-2,4,3] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2
[-1,-2,4,-3] => [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? = 5
[-1,-2,-4,3] => [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? = 5
[-1,-2,-4,-3] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2
[1,3,-2,4] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2
[1,3,-2,-4] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 4
[1,-3,2,4] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2
[1,-3,2,-4] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 4
[-1,3,2,-4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2
[-1,3,-2,4] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 4
[-1,3,-2,-4] => [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? = 5
[-1,-3,2,4] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 4
[-1,-3,2,-4] => [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? = 5
[-1,-3,-2,-4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2
[1,3,4,-2] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[1,3,-4,2] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[1,-3,4,2] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[1,-3,-4,-2] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-1,3,4,-2] => [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? = 5
[-1,3,-4,2] => [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? = 5
[-1,-3,4,2] => [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? = 5
[-1,-3,-4,-2] => [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? = 5
[1,4,2,-3] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[1,4,-2,3] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[1,-4,2,3] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[1,-4,-2,-3] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-1,4,2,-3] => [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? = 5
[-1,4,-2,3] => [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? = 5
[2,-1,4,-3] => [2,2]
=> [[2,2],[]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[2,-1,-4,3] => [2,2]
=> [[2,2],[]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[-2,1,4,-3] => [2,2]
=> [[2,2],[]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[-2,1,-4,3] => [2,2]
=> [[2,2],[]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[2,3,-1,4] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[2,-3,1,4] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-2,3,1,4] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-2,-3,-1,4] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[2,3,4,-1] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[2,3,-4,1] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[2,-3,4,1] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[2,-3,-4,-1] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[-2,3,4,1] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[-2,3,-4,-1] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[-2,-3,4,-1] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[-2,-3,-4,1] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[2,4,1,-3] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[2,4,-1,3] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[2,-4,1,3] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[2,-4,-1,-3] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[-2,4,1,3] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[-2,4,-1,-3] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[-2,-4,1,-3] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[-2,-4,-1,3] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[2,4,3,-1] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[2,-4,3,1] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-2,4,3,1] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[-2,-4,3,-1] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
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