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Your data matches 26 different statistics following compositions of up to 3 maps.
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Matching statistic: St000551
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(load all 3 compositions to match this statistic)
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St000551: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St000551: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1,1],[1,1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1,1],[1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2,1],[1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2,1],[2,1]]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [[4,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2,1],[1,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [[4,3,1],[2]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3,1],[2,1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [[4,3,1],[1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [[3,2,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2,1],[2]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [[3,3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [[3,3,2,2],[2,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [[4,3,2],[2,1]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [[4,4,2],[3,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [[4,4,2],[2,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [[3,3,3,2],[2,1,1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [[4,3,2],[1,1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [[4,3,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [[4,4,3],[3,1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [[4,4,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,0,1,1,0,0,1,0]
=> [[3,3,2,2],[2,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [[3,3,2,2],[1,1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,1,0,0,1,1,0,0]
=> [[4,3,2],[2]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [[4,4,2],[2]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,1,1,0,0,0,1,0]
=> [[3,3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [[4,3,2],[1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1,1,1],[1,1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1,1,1],[1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [[2,2,2,2,1,1],[1,1,1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2,1,1],[1,1]]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2,1,1],[2,1]]
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [[4,2,1,1],[1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [[3,3,3,1,1],[2,2]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=> [[4,3,1,1],[2]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=> [[3,2,2,2,1],[1,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=> [[3,3,2,2,1],[2,1,1]]
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
=> [[4,2,2,1],[1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=> [[3,3,3,2,1],[2,2,1]]
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> [[4,3,2,1],[2,1]]
=> ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> 6
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
=> [[4,4,2,1],[3,1]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 5
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
=> [[5,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=> [[4,3,3,1],[2,2]]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=> [[4,4,3,1],[3,2]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 5
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=> [[5,3,1],[2]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
Description
The number of left modular elements of a lattice.
A pair $(x, y)$ of elements of a lattice $L$ is a modular pair if for every $z\geq y$ we have that $(y\vee x) \wedge z = y \vee (x \wedge z)$. An element $x$ is left-modular if $(x, y)$ is a modular pair for every $y\in L$.
Matching statistic: St000550
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
St000550: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
St000550: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1,1],[1,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2,1],[1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2,1],[2,1]]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [[4,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2,1],[1,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [[4,3,1],[2]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3,1],[2,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [[4,3,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [[3,2,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2,1],[2]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [[3,3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [[3,3,2,2],[2,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [[4,3,2],[2,1]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [[4,4,2],[3,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [[4,4,2],[2,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [[3,3,3,2],[2,1,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [[4,3,2],[1,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [[4,3,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [[4,4,3],[3,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [[4,4,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,0,1,1,0,0,1,0]
=> [[3,3,2,2],[2,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [[3,3,2,2],[1,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,1,0,0,1,1,0,0]
=> [[4,3,2],[2]]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [[4,4,2],[2]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,1,1,0,0,0,1,0]
=> [[3,3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [[4,3,2],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1,1,1],[1,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1,1,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [[2,2,2,2,1,1],[1,1,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2,1,1],[1,1]]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2,1,1],[2,1]]
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [[4,2,1,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [[3,3,3,1,1],[2,2]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=> [[4,3,1,1],[2]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=> [[3,2,2,2,1],[1,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=> [[3,3,2,2,1],[2,1,1]]
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
=> [[4,2,2,1],[1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=> [[3,3,3,2,1],[2,2,1]]
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> [[4,3,2,1],[2,1]]
=> ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 6
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
=> [[4,4,2,1],[3,1]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
=> [[5,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=> [[4,3,3,1],[2,2]]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=> [[4,4,3,1],[3,2]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=> [[5,3,1],[2]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
Description
The number of modular elements of a lattice.
A pair $(x, y)$ of elements of a lattice $L$ is a modular pair if for every $z\geq y$ we have that $(y\vee x) \wedge z = y \vee (x \wedge z)$. An element $x$ is left-modular if $(x, y)$ is a modular pair for every $y\in L$, and is modular if both $(x, y)$ and $(y, x)$ are modular pairs for every $y\in L$.
Matching statistic: St001616
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
St001616: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
St001616: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1,1],[1,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2,1],[1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2,1],[2,1]]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [[4,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2,1],[1,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [[4,3,1],[2]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3,1],[2,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [[4,3,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [[3,2,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2,1],[2]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [[3,3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [[3,3,2,2],[2,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [[4,3,2],[2,1]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [[4,4,2],[3,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [[4,4,2],[2,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [[3,3,3,2],[2,1,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [[4,3,2],[1,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [[4,3,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [[4,4,3],[3,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [[4,4,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,0,1,1,0,0,1,0]
=> [[3,3,2,2],[2,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [[3,3,2,2],[1,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,1,0,0,1,1,0,0]
=> [[4,3,2],[2]]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [[4,4,2],[2]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,1,1,0,0,0,1,0]
=> [[3,3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [[4,3,2],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1,1,1],[1,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1,1,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [[2,2,2,2,1,1],[1,1,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2,1,1],[1,1]]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2,1,1],[2,1]]
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [[4,2,1,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [[3,3,3,1,1],[2,2]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=> [[4,3,1,1],[2]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=> [[3,2,2,2,1],[1,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=> [[3,3,2,2,1],[2,1,1]]
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
=> [[4,2,2,1],[1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=> [[3,3,3,2,1],[2,2,1]]
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> [[4,3,2,1],[2,1]]
=> ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 6
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
=> [[4,4,2,1],[3,1]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
=> [[5,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=> [[4,3,3,1],[2,2]]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=> [[4,4,3,1],[3,2]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=> [[5,3,1],[2]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
Description
The number of neutral elements in a lattice.
An element $e$ of the lattice $L$ is neutral if the sublattice generated by $e$, $x$ and $y$ is distributive for all $x, y \in L$.
Matching statistic: St001880
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1,1],[1,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2,1],[1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2,1],[2,1]]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [[4,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2,1],[1,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [[4,3,1],[2]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3,1],[2,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [[4,3,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [[3,2,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2,1],[2]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [[3,3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [[3,3,2,2],[2,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [[4,3,2],[2,1]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [[4,4,2],[3,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [[4,4,2],[2,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [[3,3,3,2],[2,1,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [[4,3,2],[1,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [[4,3,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [[4,4,3],[3,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [[4,4,3],[2,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,0,1,1,0,0,1,0]
=> [[3,3,2,2],[2,1]]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [[3,3,2,2],[1,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,1,0,0,1,1,0,0]
=> [[4,3,2],[2]]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [[4,4,2],[2]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,1,1,0,0,0,1,0]
=> [[3,3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [[4,3,2],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1,1,1],[1,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1,1,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [[2,2,2,2,1,1],[1,1,1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2,1,1],[1,1]]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2,1,1],[2,1]]
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [[4,2,1,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [[3,3,3,1,1],[2,2]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=> [[4,3,1,1],[2]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=> [[3,2,2,2,1],[1,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=> [[3,3,2,2,1],[2,1,1]]
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
=> [[4,2,2,1],[1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=> [[3,3,3,2,1],[2,2,1]]
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> [[4,3,2,1],[2,1]]
=> ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> 6
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
=> [[4,4,2,1],[3,1]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 5
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
=> [[5,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=> [[4,3,3,1],[2,2]]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=> [[4,4,3,1],[3,2]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 5
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=> [[5,3,1],[2]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St001198
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00142: Dyck paths —promotion⟶ Dyck paths
St001198: Dyck paths ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 40%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00142: Dyck paths —promotion⟶ Dyck paths
St001198: Dyck paths ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 40%
Values
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> 2 = 3 - 1
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,0,1,1,1,0,0,0]
=> 2 = 3 - 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
=> ? = 3 - 1
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
=> ? = 3 - 1
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1,1]
=> [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
=> ? = 4 - 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
=> ? = 5 - 1
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
=> ? = 3 - 1
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
=> ? = 4 - 1
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1,1]
=> [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
=> ? = 4 - 1
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,2,2,1,1]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
=> ? = 3 - 1
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
=> ? = 3 - 1
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
=> ? = 3 - 1
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
=> ? = 3 - 1
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=> ? = 3 - 1
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2]
=> [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 4 - 1
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
=> ? = 3 - 1
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,1,0,0,0]
=> ? = 5 - 1
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2]
=> [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
=> ? = 4 - 1
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> 3 = 4 - 1
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
=> ? = 3 - 1
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2]
=> [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,0,1,1,1,0,1,0,0,0]
=> ? = 3 - 1
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]
=> ? = 3 - 1
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=> ? = 3 - 1
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
=> ? = 3 - 1
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
=> ? = 3 - 1
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> 2 = 3 - 1
[1,1,1,0,0,0,1,1,0,0,1,0]
=> [5,3,3]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> ? = 4 - 1
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> 2 = 3 - 1
[1,1,1,0,0,1,0,0,1,1,0,0]
=> [4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> 3 = 4 - 1
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> 2 = 3 - 1
[1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,0,1,1,1,0,0,0]
=> ? = 3 - 1
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,0,1,1,1,0,0,0]
=> 2 = 3 - 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,2,1]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,2,1]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,2,1]
=> [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,2,1]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 5 - 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,2,1]
=> [1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 6 - 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [5,4,4,2,2,1]
=> [1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,2,1]
=> [1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 4 - 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=> [5,5,4,3,1,1]
=> [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 4 - 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,1,1]
=> [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 6 - 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
=> [5,4,4,3,1,1]
=> [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 4 - 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,1,1]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 6 - 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,1,1]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 6 - 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
=> [6,4,3,3,1,1]
=> [1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 5 - 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
=> [5,4,3,3,1,1]
=> [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 3 - 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,1,1]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
=> ? = 4 - 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,1,1]
=> [1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> ?
=> ? = 5 - 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=> [5,4,4,2,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> ?
=> ? = 5 - 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,1,1]
=> [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
=> ?
=> ? = 4 - 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 3 - 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,2]
=> [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 4 - 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,2]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 5 - 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,2]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 5 - 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
=> [6,4,3,3,2]
=> [1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 4 - 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,2]
=> [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
=> ?
=> ? = 3 - 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,2]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
=> ?
=> ? = 5 - 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> 2 = 3 - 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> 3 = 4 - 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> 2 = 3 - 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
=> [4,4,3]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> 2 = 3 - 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> 2 = 3 - 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
=> [4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> 3 = 4 - 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> 2 = 3 - 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,0,1,1,1,0,0,0]
=> 2 = 3 - 1
Description
The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Matching statistic: St001206
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00142: Dyck paths —promotion⟶ Dyck paths
St001206: Dyck paths ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 40%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00142: Dyck paths —promotion⟶ Dyck paths
St001206: Dyck paths ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 40%
Values
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> 2 = 3 - 1
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,0,1,1,1,0,0,0]
=> 2 = 3 - 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
=> ? = 3 - 1
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
=> ? = 3 - 1
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1,1]
=> [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
=> ? = 4 - 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
=> ? = 5 - 1
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
=> ? = 3 - 1
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
=> ? = 4 - 1
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1,1]
=> [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
=> ? = 4 - 1
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,2,2,1,1]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
=> ? = 3 - 1
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
=> ? = 3 - 1
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
=> ? = 3 - 1
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
=> ? = 3 - 1
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=> ? = 3 - 1
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2]
=> [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 4 - 1
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
=> ? = 3 - 1
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,1,0,0,0]
=> ? = 5 - 1
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2]
=> [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
=> ? = 4 - 1
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> 3 = 4 - 1
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
=> ? = 3 - 1
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2]
=> [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,0,1,1,1,0,1,0,0,0]
=> ? = 3 - 1
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]
=> ? = 3 - 1
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=> ? = 3 - 1
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
=> ? = 3 - 1
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
=> ? = 3 - 1
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> 2 = 3 - 1
[1,1,1,0,0,0,1,1,0,0,1,0]
=> [5,3,3]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> ? = 4 - 1
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> 2 = 3 - 1
[1,1,1,0,0,1,0,0,1,1,0,0]
=> [4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> 3 = 4 - 1
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> 2 = 3 - 1
[1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,0,1,1,1,0,0,0]
=> ? = 3 - 1
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,0,1,1,1,0,0,0]
=> 2 = 3 - 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,2,1]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,2,1]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,2,1]
=> [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,2,1]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 5 - 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,2,1]
=> [1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 6 - 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [5,4,4,2,2,1]
=> [1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,2,1]
=> [1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 4 - 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=> [5,5,4,3,1,1]
=> [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 4 - 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,1,1]
=> [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 6 - 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
=> [5,4,4,3,1,1]
=> [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 4 - 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,1,1]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 6 - 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,1,1]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 6 - 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
=> [6,4,3,3,1,1]
=> [1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 5 - 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
=> [5,4,3,3,1,1]
=> [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 3 - 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,1,1]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
=> ? = 4 - 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,1,1]
=> [1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> ?
=> ? = 5 - 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=> [5,4,4,2,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> ?
=> ? = 5 - 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,1,1]
=> [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
=> ?
=> ? = 4 - 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 3 - 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,2]
=> [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 4 - 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,2]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 5 - 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,2]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 5 - 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
=> [6,4,3,3,2]
=> [1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 4 - 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,2]
=> [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
=> ?
=> ? = 3 - 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,2]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
=> ?
=> ? = 5 - 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> 2 = 3 - 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> 3 = 4 - 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> 2 = 3 - 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
=> [4,4,3]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> 2 = 3 - 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> 2 = 3 - 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
=> [4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> 3 = 4 - 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> 2 = 3 - 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,0,1,1,1,0,0,0]
=> 2 = 3 - 1
Description
The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$.
Matching statistic: St001006
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
St001006: Dyck paths ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 40%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
St001006: Dyck paths ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 40%
Values
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> 1 = 3 - 2
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 3 - 2
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
=> ? = 3 - 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
=> ? = 3 - 2
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1,1]
=> [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]
=> ? = 4 - 2
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0]
=> ? = 5 - 2
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
=> ? = 3 - 2
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
=> ? = 4 - 2
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1,1]
=> [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
=> ? = 4 - 2
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,2,2,1,1]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0]
=> ? = 3 - 2
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
=> ? = 3 - 2
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
=> ? = 3 - 2
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0]
=> ? = 3 - 2
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
=> ? = 3 - 2
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2]
=> [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
=> ? = 4 - 2
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]
=> ? = 3 - 2
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> ? = 5 - 2
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2]
=> [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
=> ? = 4 - 2
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> 2 = 4 - 2
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
=> ? = 3 - 2
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2]
=> [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
=> ? = 3 - 2
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
=> ? = 3 - 2
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
=> ? = 3 - 2
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
=> ? = 3 - 2
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
=> ? = 3 - 2
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> 1 = 3 - 2
[1,1,1,0,0,0,1,1,0,0,1,0]
=> [5,3,3]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
=> ? = 4 - 2
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 1 = 3 - 2
[1,1,1,0,0,1,0,0,1,1,0,0]
=> [4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> 2 = 4 - 2
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> 1 = 3 - 2
[1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
=> ? = 3 - 2
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 3 - 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,2,1]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,2,1]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,2,1]
=> [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,2,1]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 5 - 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,2,1]
=> [1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 6 - 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [5,4,4,2,2,1]
=> [1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,2,1]
=> [1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 4 - 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=> [5,5,4,3,1,1]
=> [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 4 - 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,1,1]
=> [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 6 - 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
=> [5,4,4,3,1,1]
=> [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 4 - 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,1,1]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 6 - 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,1,1]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 6 - 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
=> [6,4,3,3,1,1]
=> [1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 5 - 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
=> [5,4,3,3,1,1]
=> [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 3 - 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,1,1]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0]
=> ? = 4 - 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,1,1]
=> [1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> ?
=> ? = 5 - 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=> [5,4,4,2,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> ?
=> ? = 5 - 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,1,1]
=> [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
=> ?
=> ? = 4 - 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 3 - 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,2]
=> [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 4 - 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,2]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 5 - 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,2]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
=> [1,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
=> ? = 5 - 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
=> [6,4,3,3,2]
=> [1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 4 - 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,2]
=> [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
=> ?
=> ? = 3 - 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,2]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
=> ? = 5 - 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> 1 = 3 - 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> 2 = 4 - 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> 1 = 3 - 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
=> [4,4,3]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> 1 = 3 - 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 1 = 3 - 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
=> [4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> 2 = 4 - 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> 1 = 3 - 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 3 - 2
Description
Number of simple modules with projective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path.
Matching statistic: St001202
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00124: Dyck paths —Adin-Bagno-Roichman transformation⟶ Dyck paths
St001202: Dyck paths ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 40%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00124: Dyck paths —Adin-Bagno-Roichman transformation⟶ Dyck paths
St001202: Dyck paths ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 40%
Values
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,1,0,0]
=> 1 = 3 - 2
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 1 = 3 - 2
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]
=> ? = 3 - 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]
=> ? = 3 - 2
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1,1]
=> [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]
=> ? = 4 - 2
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0]
=> ? = 5 - 2
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
=> ? = 3 - 2
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
=> ? = 4 - 2
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1,1]
=> [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]
=> ? = 4 - 2
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,2,2,1,1]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
=> ? = 3 - 2
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
=> ? = 3 - 2
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
=> ? = 3 - 2
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
=> ? = 3 - 2
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,1,0,0]
=> ? = 3 - 2
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2]
=> [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
=> ? = 4 - 2
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
=> ? = 3 - 2
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 5 - 2
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2]
=> [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
=> ? = 4 - 2
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> 2 = 4 - 2
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
=> ? = 3 - 2
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2]
=> [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
=> ? = 3 - 2
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
=> ? = 3 - 2
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,1,0,0]
=> ? = 3 - 2
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,1,0,0]
=> ? = 3 - 2
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
=> ? = 3 - 2
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,1,0,0]
=> 1 = 3 - 2
[1,1,1,0,0,0,1,1,0,0,1,0]
=> [5,3,3]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> ? = 4 - 2
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> 1 = 3 - 2
[1,1,1,0,0,1,0,0,1,1,0,0]
=> [4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> 2 = 4 - 2
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 1 = 3 - 2
[1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=> ? = 3 - 2
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 1 = 3 - 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,2,1]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,2,1]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,2,1]
=> [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,2,1]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 5 - 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,2,1]
=> [1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 6 - 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [5,4,4,2,2,1]
=> [1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,2,1]
=> [1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 4 - 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=> [5,5,4,3,1,1]
=> [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 4 - 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,1,1]
=> [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 6 - 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
=> [5,4,4,3,1,1]
=> [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 4 - 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,1,1]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 6 - 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,1,1]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 6 - 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
=> [6,4,3,3,1,1]
=> [1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 5 - 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
=> [5,4,3,3,1,1]
=> [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 3 - 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,1,1]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,1,0,0]
=> ? = 4 - 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,1,1]
=> [1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> ?
=> ? = 5 - 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=> [5,4,4,2,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> ?
=> ? = 5 - 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,1,1]
=> [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
=> ?
=> ? = 4 - 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 3 - 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,2]
=> [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 4 - 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,2]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 5 - 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,2]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 5 - 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
=> [6,4,3,3,2]
=> [1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 4 - 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,2]
=> [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
=> ?
=> ? = 3 - 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,2]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
=> ?
=> ? = 5 - 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> 1 = 3 - 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> 2 = 4 - 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,1,0,0]
=> 1 = 3 - 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
=> [4,4,3]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> 1 = 3 - 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> 1 = 3 - 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
=> [4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> 2 = 4 - 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 1 = 3 - 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 1 = 3 - 2
Description
Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n−1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a special CNakayama algebra.
Associate to this special CNakayama algebra a Dyck path as follows:
In the list L delete the first entry $c_0$ and substract from all other entries $n$−1 and then append the last element 1. The result is a Kupisch series of an LNakayama algebra to which we can associate a Dyck path as the top boundary of the Auslander-Reiten quiver of the LNakayama algebra.
The statistic gives half the dominant dimension of hte first indecomposable projective module in the special CNakayama algebra.
Matching statistic: St001113
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00143: Dyck paths —inverse promotion⟶ Dyck paths
St001113: Dyck paths ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 40%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00143: Dyck paths —inverse promotion⟶ Dyck paths
St001113: Dyck paths ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 40%
Values
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> 0 = 3 - 3
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> 0 = 3 - 3
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> [1,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0,0]
=> ? = 3 - 3
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
=> ? = 3 - 3
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1,1]
=> [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
=> ? = 4 - 3
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
=> ? = 5 - 3
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
=> ? = 3 - 3
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
=> ? = 4 - 3
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1,1]
=> [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 4 - 3
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,2,2,1,1]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
=> ? = 3 - 3
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
=> ? = 3 - 3
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 3 - 3
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
=> ? = 3 - 3
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 3 - 3
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2]
=> [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
=> ? = 4 - 3
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
=> ? = 3 - 3
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0,1,0]
=> ? = 5 - 3
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2]
=> [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> ? = 4 - 3
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,0,0,1,0]
=> 1 = 4 - 3
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 3 - 3
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2]
=> [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 3 - 3
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
=> ? = 3 - 3
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
=> ? = 3 - 3
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
=> ? = 3 - 3
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
=> ? = 3 - 3
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> 0 = 3 - 3
[1,1,1,0,0,0,1,1,0,0,1,0]
=> [5,3,3]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4 - 3
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> 0 = 3 - 3
[1,1,1,0,0,1,0,0,1,1,0,0]
=> [4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,0,0,0,1,0]
=> 1 = 4 - 3
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> 0 = 3 - 3
[1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 3
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> 0 = 3 - 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,2,1]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,2,1]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,2,1]
=> [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,2,1]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 5 - 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,2,1]
=> [1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 6 - 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [5,4,4,2,2,1]
=> [1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,2,1]
=> [1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 4 - 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=> [5,5,4,3,1,1]
=> [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 4 - 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,1,1]
=> [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 6 - 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
=> [5,4,4,3,1,1]
=> [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 4 - 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,1,1]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 6 - 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,1,1]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 6 - 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
=> [6,4,3,3,1,1]
=> [1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 5 - 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
=> [5,4,3,3,1,1]
=> [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 3 - 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,1,1]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,1,0]
=> ? = 4 - 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,1,1]
=> [1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> ?
=> ? = 5 - 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=> [5,4,4,2,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> ?
=> ? = 5 - 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,1,1]
=> [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
=> ?
=> ? = 4 - 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 3 - 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,2]
=> [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 4 - 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,2]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 5 - 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,2]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 5 - 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
=> [6,4,3,3,2]
=> [1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 4 - 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,2]
=> [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
=> ?
=> ? = 3 - 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,2]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
=> ?
=> ? = 5 - 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> 0 = 3 - 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,0,0,1,0]
=> 1 = 4 - 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> 0 = 3 - 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
=> [4,4,3]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> 0 = 3 - 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> 0 = 3 - 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
=> [4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,0,0,0,1,0]
=> 1 = 4 - 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> 0 = 3 - 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> 0 = 3 - 3
Description
Number of indecomposable projective non-injective modules with reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra.
Matching statistic: St001217
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00229: Dyck paths —Delest-Viennot⟶ Dyck paths
St001217: Dyck paths ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 40%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00229: Dyck paths —Delest-Viennot⟶ Dyck paths
St001217: Dyck paths ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 40%
Values
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 0 = 3 - 3
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> 0 = 3 - 3
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> [1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
=> ? = 3 - 3
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
=> [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
=> ? = 3 - 3
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1,1]
=> [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
=> ? = 4 - 3
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 5 - 3
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 3 - 3
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 4 - 3
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1,1]
=> [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
=> [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
=> ? = 4 - 3
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,2,2,1,1]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 3 - 3
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1,1]
=> [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 3 - 3
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
=> ? = 3 - 3
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
=> ? = 3 - 3
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
=> ? = 3 - 3
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2]
=> [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
=> ? = 4 - 3
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2]
=> [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
=> ? = 3 - 3
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
=> ? = 5 - 3
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2]
=> [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
=> ? = 4 - 3
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 4 - 3
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> ? = 3 - 3
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2]
=> [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> ? = 3 - 3
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 3 - 3
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 3 - 3
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
=> ? = 3 - 3
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
=> ? = 3 - 3
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 0 = 3 - 3
[1,1,1,0,0,0,1,1,0,0,1,0]
=> [5,3,3]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 4 - 3
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> 0 = 3 - 3
[1,1,1,0,0,1,0,0,1,1,0,0]
=> [4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> 1 = 4 - 3
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> 0 = 3 - 3
[1,1,1,0,0,1,1,0,0,0,1,0]
=> [5,2,2]
=> [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
=> ? = 3 - 3
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> 0 = 3 - 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,2,1]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,2,1]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,2,1]
=> [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,2,1]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 5 - 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,2,1]
=> [1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 6 - 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [5,4,4,2,2,1]
=> [1,0,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,2,1]
=> [1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 3 - 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,2,1]
=> [1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
=> ?
=> ? = 4 - 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=> [5,5,4,3,1,1]
=> [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 4 - 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,1,1]
=> [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 6 - 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
=> [5,4,4,3,1,1]
=> [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 4 - 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,1,1]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 6 - 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,1,1]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 6 - 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
=> [6,4,3,3,1,1]
=> [1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 5 - 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
=> [5,4,3,3,1,1]
=> [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ?
=> ? = 3 - 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,1,1]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> [1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0,0,0]
=> ? = 4 - 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,1,1]
=> [1,0,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> ?
=> ? = 5 - 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=> [5,4,4,2,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]
=> ?
=> ? = 5 - 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,1,1]
=> [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
=> ?
=> ? = 4 - 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
=> ? = 3 - 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,2]
=> [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 4 - 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,2]
=> [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 5 - 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,2]
=> [1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,0]
=> ? = 5 - 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
=> [6,4,3,3,2]
=> [1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
=> ?
=> ? = 4 - 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,2]
=> [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
=> ?
=> ? = 3 - 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,2]
=> [1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> 0 = 3 - 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,3,2,2]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 4 - 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [3,3,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 0 = 3 - 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
=> [4,4,3]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0,1,0]
=> 0 = 3 - 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [3,3,3]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> 0 = 3 - 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
=> [4,4,2]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> 1 = 4 - 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
=> [3,3,2]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> 0 = 3 - 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
=> [4,2,2]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> 0 = 3 - 3
Description
The projective dimension of the indecomposable injective module I[n-2] in the corresponding Nakayama algebra with simples enumerated from 0 to n-1.
The following 16 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001230The number of simple modules with injective dimension equal to the dominant dimension equal to one and the dual property. St000758The length of the longest staircase fitting into an integer composition. St000820The number of compositions obtained by rotating the composition. St000657The smallest part of an integer composition. St000455The second largest eigenvalue of a graph if it is integral. St000763The sum of the positions of the strong records of an integer composition. St000805The number of peaks of the associated bargraph. St000900The minimal number of repetitions of a part in an integer composition. St000902 The minimal number of repetitions of an integer composition. St000905The number of different multiplicities of parts of an integer composition. St000968We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n−1}]$ by adding $c_0$ to $c_{n−1}$. St001256Number of simple reflexive modules that are 2-stable reflexive. St001493The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra. St000761The number of ascents in an integer composition. St001221The number of simple modules in the corresponding LNakayama algebra that have 2 dimensional second Extension group with the regular module. St001292The injective dimension of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path.
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