- FindStat

Your data matches 27 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St001877

Mapping

Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001877: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

{{1,2},{3,4},{5}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2},{3,5},{4}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3},{2,4},{5}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3},{2,5},{4}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,4},{2,3},{5}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,5},{2,3},{4}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1},{2,3},{4,5}}
 => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,4},{2,5},{3}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,5},{2,4},{3}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1},{2,4},{3,5}}
 => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1},{2,5},{3,4}}
 => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,3},{4,5,6}}
 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,3},{4,5},{6}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,3},{4,6},{5}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,4},{3,5,6}}
 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,4},{3,5},{6}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,4},{3,6},{5}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,5},{3,4,6}}
 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,5},{3,4},{6}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,6},{3,4,5}}
 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2},{3,4,5},{6}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
{{1,2,6},{3,4},{5}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2},{3,4,6},{5}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
{{1,2},{3,4},{5,6}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
{{1,2},{3,4},{5},{6}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,5},{3,6},{4}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,6},{3,5},{4}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2},{3,5,6},{4}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
{{1,2},{3,5},{4,6}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
{{1,2},{3,5},{4},{6}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2},{3,6},{4,5}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
{{1,2},{3},{4,5},{6}}
 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
{{1,2},{3,6},{4},{5}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2},{3},{4,6},{5}}
 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
{{1,3,4},{2,5,6}}
 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3,4},{2,5},{6}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3,4},{2,6},{5}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3,5},{2,4,6}}
 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3,5},{2,4},{6}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3,6},{2,4,5}}
 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3},{2,4,5},{6}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
{{1,3,6},{2,4},{5}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3},{2,4,6},{5}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
{{1,3},{2,4},{5,6}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
{{1,3},{2,4},{5},{6}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3,5},{2,6},{4}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3,6},{2,5},{4}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3},{2,5,6},{4}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
{{1,3},{2,5},{4,6}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
{{1,3},{2,5},{4},{6}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,2),(2,1)],3)
 => 0

Description

Number of indecomposable injective modules with projective dimension 2.

Matching statistic: St001876

Mapping

Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001876: Lattices ⟶ ℤResult quality: 75% ●values known / values provided: 76%●distinct values known / distinct values provided: 75%

Values

{{1,2},{3,4},{5}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2},{3,5},{4}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3},{2,4},{5}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3},{2,5},{4}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,4},{2,3},{5}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,5},{2,3},{4}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1},{2,3},{4,5}}
 => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,4},{2,5},{3}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,5},{2,4},{3}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1},{2,4},{3,5}}
 => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1},{2,5},{3,4}}
 => [1,2,2] => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,3},{4,5,6}}
 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,3},{4,5},{6}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,3},{4,6},{5}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,4},{3,5,6}}
 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,4},{3,5},{6}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,4},{3,6},{5}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,5},{3,4,6}}
 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,5},{3,4},{6}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,6},{3,4,5}}
 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2},{3,4,5},{6}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
{{1,2,6},{3,4},{5}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2},{3,4,6},{5}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
{{1,2},{3,4},{5,6}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
{{1,2},{3,4},{5},{6}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,5},{3,6},{4}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2,6},{3,5},{4}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2},{3,5,6},{4}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
{{1,2},{3,5},{4,6}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
{{1,2},{3,5},{4},{6}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2},{3,6},{4,5}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
{{1,2},{3},{4,5},{6}}
 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
{{1,2},{3,6},{4},{5}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2},{3},{4,6},{5}}
 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
{{1,3,4},{2,5,6}}
 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3,4},{2,5},{6}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3,4},{2,6},{5}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3,5},{2,4,6}}
 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3,5},{2,4},{6}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3,6},{2,4,5}}
 => [3,3] => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3},{2,4,5},{6}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
{{1,3,6},{2,4},{5}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3},{2,4,6},{5}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
{{1,3},{2,4},{5,6}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
{{1,3},{2,4},{5},{6}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3,5},{2,6},{4}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3,6},{2,5},{4}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,3},{2,5,6},{4}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
{{1,3},{2,5},{4,6}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
{{1,3},{2,5},{4},{6}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,2),(2,1)],3)
 => 0
{{1,2},{3,4},{5,6},{7}}
 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ? = 2
{{1,2},{3,4},{5,7},{6}}
 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ? = 2
{{1,2},{3,4},{5},{6,7}}
 => [2,2,1,2] => [[4,3,3,2],[2,2,1]]
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ? = 2
{{1,2},{3,5},{4,6},{7}}
 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ? = 2
{{1,2},{3,5},{4,7},{6}}
 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ? = 2
{{1,2},{3,5},{4},{6,7}}
 => [2,2,1,2] => [[4,3,3,2],[2,2,1]]
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ? = 2
{{1,2},{3,6},{4,5},{7}}
 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ? = 2
{{1,2},{3},{4,5,6},{7}}
 => [2,1,3,1] => [[4,4,2,2],[3,1,1]]
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ? = 2
{{1,2},{3,7},{4,5},{6}}
 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ? = 2
{{1,2},{3},{4,5,7},{6}}
 => [2,1,3,1] => [[4,4,2,2],[3,1,1]]
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ? = 2
{{1,2},{3},{4,5},{6,7}}
 => [2,1,2,2] => [[4,3,2,2],[2,1,1]]
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ? = 2
{{1,2},{3,6},{4,7},{5}}
 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ? = 2
{{1,2},{3,6},{4},{5,7}}
 => [2,2,1,2] => [[4,3,3,2],[2,2,1]]
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ? = 2
{{1,2},{3,7},{4,6},{5}}
 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ? = 2
{{1,2},{3},{4,6,7},{5}}
 => [2,1,3,1] => [[4,4,2,2],[3,1,1]]
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ? = 2
{{1,2},{3},{4,6},{5,7}}
 => [2,1,2,2] => [[4,3,2,2],[2,1,1]]
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ? = 2
{{1,2},{3,7},{4},{5,6}}
 => [2,2,1,2] => [[4,3,3,2],[2,2,1]]
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ? = 2
{{1,2},{3},{4,7},{5,6}}
 => [2,1,2,2] => [[4,3,2,2],[2,1,1]]
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ? = 2
{{1,3},{2,4},{5,6},{7}}
 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ? = 2
{{1,3},{2,4},{5,7},{6}}
 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ? = 2
{{1,3},{2,4},{5},{6,7}}
 => [2,2,1,2] => [[4,3,3,2],[2,2,1]]
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ? = 2
{{1,3},{2,5},{4,6},{7}}
 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ? = 2
{{1,3},{2,5},{4,7},{6}}
 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ? = 2
{{1,3},{2,5},{4},{6,7}}
 => [2,2,1,2] => [[4,3,3,2],[2,2,1]]
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ? = 2
{{1,3},{2,6},{4,5},{7}}
 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ? = 2
{{1,3},{2},{4,5,6},{7}}
 => [2,1,3,1] => [[4,4,2,2],[3,1,1]]
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ? = 2
{{1,3},{2,7},{4,5},{6}}
 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ? = 2
{{1,3},{2},{4,5,7},{6}}
 => [2,1,3,1] => [[4,4,2,2],[3,1,1]]
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ? = 2
{{1,3},{2},{4,5},{6,7}}
 => [2,1,2,2] => [[4,3,2,2],[2,1,1]]
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ? = 2
{{1,3},{2,6},{4,7},{5}}
 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ? = 2
{{1,3},{2,6},{4},{5,7}}
 => [2,2,1,2] => [[4,3,3,2],[2,2,1]]
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ? = 2
{{1,3},{2,7},{4,6},{5}}
 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ? = 2
{{1,3},{2},{4,6,7},{5}}
 => [2,1,3,1] => [[4,4,2,2],[3,1,1]]
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ? = 2
{{1,3},{2},{4,6},{5,7}}
 => [2,1,2,2] => [[4,3,2,2],[2,1,1]]
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ? = 2
{{1,3},{2,7},{4},{5,6}}
 => [2,2,1,2] => [[4,3,3,2],[2,2,1]]
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ? = 2
{{1,3},{2},{4,7},{5,6}}
 => [2,1,2,2] => [[4,3,2,2],[2,1,1]]
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ? = 2
{{1,4},{2,3},{5,6},{7}}
 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ? = 2
{{1,4},{2,3},{5,7},{6}}
 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ? = 2
{{1,4},{2,3},{5},{6,7}}
 => [2,2,1,2] => [[4,3,3,2],[2,2,1]]
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ? = 2
{{1},{2,3,4},{5,6},{7}}
 => [1,3,2,1] => [[4,4,3,1],[3,2]]
 => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ? = 2
{{1},{2,3,4},{5,7},{6}}
 => [1,3,2,1] => [[4,4,3,1],[3,2]]
 => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ? = 2
{{1},{2,3,4},{5},{6,7}}
 => [1,3,1,2] => [[4,3,3,1],[2,2]]
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ? = 2
{{1,5},{2,3},{4,6},{7}}
 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ? = 2
{{1,5},{2,3},{4,7},{6}}
 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ? = 2
{{1,5},{2,3},{4},{6,7}}
 => [2,2,1,2] => [[4,3,3,2],[2,2,1]]
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ? = 2
{{1},{2,3,5},{4,6},{7}}
 => [1,3,2,1] => [[4,4,3,1],[3,2]]
 => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ? = 2
{{1},{2,3,5},{4,7},{6}}
 => [1,3,2,1] => [[4,4,3,1],[3,2]]
 => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ? = 2
{{1},{2,3,5},{4},{6,7}}
 => [1,3,1,2] => [[4,3,3,1],[2,2]]
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ? = 2
{{1,6},{2,3},{4,5},{7}}
 => [2,2,2,1] => [[4,4,3,2],[3,2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ? = 2
{{1},{2,3,6},{4,5},{7}}
 => [1,3,2,1] => [[4,4,3,1],[3,2]]
 => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ? = 2

Description

The number of 2-regular simple modules in the incidence algebra of the lattice.

Matching statistic: St000454

Mapping

Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00173: Integer compositions —rotate front to back⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 50%

Values

{{1,2},{3,4},{5}}
 => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
{{1,2},{3,5},{4}}
 => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
{{1,3},{2,4},{5}}
 => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
{{1,3},{2,5},{4}}
 => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
{{1,4},{2,3},{5}}
 => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
{{1,5},{2,3},{4}}
 => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
{{1},{2,3},{4,5}}
 => [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
{{1,4},{2,5},{3}}
 => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
{{1,5},{2,4},{3}}
 => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
{{1},{2,4},{3,5}}
 => [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
{{1},{2,5},{3,4}}
 => [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
{{1,2,3},{4,5,6}}
 => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,2,3},{4,5},{6}}
 => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,2,3},{4,6},{5}}
 => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,2,4},{3,5,6}}
 => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,2,4},{3,5},{6}}
 => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,2,4},{3,6},{5}}
 => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,2,5},{3,4,6}}
 => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,2,5},{3,4},{6}}
 => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,2,6},{3,4,5}}
 => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,2},{3,4,5},{6}}
 => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 1 + 2
{{1,2,6},{3,4},{5}}
 => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,2},{3,4,6},{5}}
 => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 1 + 2
{{1,2},{3,4},{5,6}}
 => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
{{1,2},{3,4},{5},{6}}
 => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,2,5},{3,6},{4}}
 => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,2,6},{3,5},{4}}
 => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,2},{3,5,6},{4}}
 => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 1 + 2
{{1,2},{3,5},{4,6}}
 => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
{{1,2},{3,5},{4},{6}}
 => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,2},{3,6},{4,5}}
 => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
{{1,2},{3},{4,5},{6}}
 => [2,1,2,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
{{1,2},{3,6},{4},{5}}
 => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,2},{3},{4,6},{5}}
 => [2,1,2,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
{{1,3,4},{2,5,6}}
 => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,3,4},{2,5},{6}}
 => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,3,4},{2,6},{5}}
 => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,3,5},{2,4,6}}
 => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,3,5},{2,4},{6}}
 => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,3,6},{2,4,5}}
 => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,3},{2,4,5},{6}}
 => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 1 + 2
{{1,3,6},{2,4},{5}}
 => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,3},{2,4,6},{5}}
 => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 1 + 2
{{1,3},{2,4},{5,6}}
 => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
{{1,3},{2,4},{5},{6}}
 => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,3,5},{2,6},{4}}
 => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,3,6},{2,5},{4}}
 => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,3},{2,5,6},{4}}
 => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 1 + 2
{{1,3},{2,5},{4,6}}
 => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
{{1,3},{2,5},{4},{6}}
 => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,3},{2,6},{4,5}}
 => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
{{1,3},{2},{4,5},{6}}
 => [2,1,2,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
{{1,3},{2,6},{4},{5}}
 => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,3},{2},{4,6},{5}}
 => [2,1,2,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
{{1,4,5},{2,3,6}}
 => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,4,5},{2,3},{6}}
 => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
{{1,4},{2,3,5},{6}}
 => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 1 + 2
{{1,4},{2,3,6},{5}}
 => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 1 + 2
{{1,5},{2,3,4},{6}}
 => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 1 + 2
{{1,6},{2,3,4},{5}}
 => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 1 + 2
{{1,5},{2,3,6},{4}}
 => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 1 + 2
{{1,6},{2,3,5},{4}}
 => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 1 + 2
{{1,4},{2,5,6},{3}}
 => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 1 + 2
{{1,5},{2,4,6},{3}}
 => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 1 + 2
{{1,6},{2,4,5},{3}}
 => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 1 + 2
{{1,2,3},{4,5,6,7}}
 => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
{{1,2,3},{4,5,6},{7}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,2,3},{4,5,7},{6}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,2,3},{4,6,7},{5}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,2,4},{3,5,6,7}}
 => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
{{1,2,4},{3,5,6},{7}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,2,4},{3,5,7},{6}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,2,4},{3,6,7},{5}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,2,5},{3,4,6,7}}
 => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
{{1,2,5},{3,4,6},{7}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,2,5},{3,4,7},{6}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,2,6},{3,4,5,7}}
 => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
{{1,2,6},{3,4,5},{7}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,2,7},{3,4,5,6}}
 => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
{{1,2,7},{3,4,5},{6}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,2,6},{3,4,7},{5}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,2,7},{3,4,6},{5}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,2,5},{3,6,7},{4}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,2,6},{3,5,7},{4}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,2,7},{3,5,6},{4}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,3,4},{2,5,6,7}}
 => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
{{1,3,4},{2,5,6},{7}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,3,4},{2,5,7},{6}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,3,4},{2,6,7},{5}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,3,5},{2,4,6,7}}
 => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
{{1,3,5},{2,4,6},{7}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,3,5},{2,4,7},{6}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,3,6},{2,4,5,7}}
 => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
{{1,3,6},{2,4,5},{7}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,3,7},{2,4,5,6}}
 => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
{{1,3,7},{2,4,5},{6}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,3,6},{2,4,7},{5}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,3,7},{2,4,6},{5}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,3,5},{2,6,7},{4}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
{{1,3,6},{2,5,7},{4}}
 => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2

Description

The largest eigenvalue of a graph if it is integral. If a graph is

$d$ -regular, then its largest eigenvalue equals

$d$ . One can show that the largest eigenvalue always lies between the average degree and the maximal degree. This statistic is undefined if the largest eigenvalue of the graph is not integral.

Matching statistic: St001001

Mapping

Mp00079: Set partitions —shape⟶ Integer partitions
Mp00312: Integer partitions —Glaisher-Franklin⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001001: Dyck paths ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 25%

Values

{{1,2},{3,4},{5}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 0
{{1,2},{3,5},{4}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 0
{{1,3},{2,4},{5}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 0
{{1,3},{2,5},{4}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 0
{{1,4},{2,3},{5}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 0
{{1,5},{2,3},{4}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 0
{{1},{2,3},{4,5}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 0
{{1,4},{2,5},{3}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 0
{{1,5},{2,4},{3}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 0
{{1},{2,4},{3,5}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 0
{{1},{2,5},{3,4}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 0
{{1,2,3},{4,5,6}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
{{1,2,3},{4,5},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0
{{1,2,3},{4,6},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0
{{1,2,4},{3,5,6}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
{{1,2,4},{3,5},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0
{{1,2,4},{3,6},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0
{{1,2,5},{3,4,6}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
{{1,2,5},{3,4},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0
{{1,2,6},{3,4,5}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
{{1,2},{3,4,5},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1
{{1,2,6},{3,4},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0
{{1,2},{3,4,6},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1
{{1,2},{3,4},{5,6}}
 => [2,2,2]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1
{{1,2},{3,4},{5},{6}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0
{{1,2,5},{3,6},{4}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0
{{1,2,6},{3,5},{4}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0
{{1,2},{3,5,6},{4}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1
{{1,2},{3,5},{4,6}}
 => [2,2,2]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1
{{1,2},{3,5},{4},{6}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0
{{1,2},{3,6},{4,5}}
 => [2,2,2]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1
{{1,2},{3},{4,5},{6}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 1
{{1,2},{3,6},{4},{5}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0
{{1,2},{3},{4,6},{5}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 1
{{1,3,4},{2,5,6}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
{{1,3,4},{2,5},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0
{{1,3,4},{2,6},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0
{{1,3,5},{2,4,6}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
{{1,3,5},{2,4},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0
{{1,3,6},{2,4,5}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
{{1,3},{2,4,5},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1
{{1,3,6},{2,4},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0
{{1,3},{2,4,6},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1
{{1,3},{2,4},{5,6}}
 => [2,2,2]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1
{{1,3},{2,4},{5},{6}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0
{{1,3,5},{2,6},{4}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0
{{1,3,6},{2,5},{4}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0
{{1,3},{2,5,6},{4}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1
{{1,3},{2,5},{4,6}}
 => [2,2,2]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1
{{1,3},{2,5},{4},{6}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0
{{1,3},{2,6},{4,5}}
 => [2,2,2]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1
{{1,3},{2},{4,5},{6}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 1
{{1,3},{2,6},{4},{5}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0
{{1,3},{2},{4,6},{5}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 1
{{1,4,5},{2,3,6}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
{{1,4,5},{2,3},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0
{{1,4,6},{2,3,5}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
{{1,4},{2,3,5},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1
{{1,4,6},{2,3},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0
{{1,4},{2,3,6},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1
{{1,4},{2,3},{5,6}}
 => [2,2,2]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1
{{1,2,3,4},{5,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,2,3,5},{4,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,2,3,6},{4,5,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,2,3,7},{4,5,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,2,3},{4,5,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,2,4,5},{3,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,2,4,6},{3,5,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,2,4,7},{3,5,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,2,4},{3,5,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,2,5,6},{3,4,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,2,5,7},{3,4,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,2,5},{3,4,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,2,6,7},{3,4,5}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,2,6},{3,4,5,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,2,7},{3,4,5,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,3,4,5},{2,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,3,4,6},{2,5,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,3,4,7},{2,5,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,3,4},{2,5,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,3,5,6},{2,4,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,3,5,7},{2,4,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,3,5},{2,4,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,3,6,7},{2,4,5}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,3,6},{2,4,5,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,3,7},{2,4,5,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,4,5,6},{2,3,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,4,5,7},{2,3,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,4,5},{2,3,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,4,6,7},{2,3,5}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,4,6},{2,3,5,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,4,7},{2,3,5,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,5,6,7},{2,3,4}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,5,6},{2,3,4,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,5,7},{2,3,4,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1,6,7},{2,3,4,5}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
{{1},{2},{3,4,5},{6},{7}}
 => [3,1,1,1,1]
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => 0
{{1},{2},{3,4,6},{5},{7}}
 => [3,1,1,1,1]
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => 0
{{1},{2},{3,4,7},{5},{6}}
 => [3,1,1,1,1]
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => 0
{{1},{2},{3,5,6},{4},{7}}
 => [3,1,1,1,1]
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => 0

Description

The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path.

Matching statistic: St001195

Mapping

Mp00079: Set partitions —shape⟶ Integer partitions
Mp00312: Integer partitions —Glaisher-Franklin⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001195: Dyck paths ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 25%

Values

{{1,2},{3,4},{5}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1 = 0 + 1
{{1,2},{3,5},{4}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1 = 0 + 1
{{1,3},{2,4},{5}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1 = 0 + 1
{{1,3},{2,5},{4}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1 = 0 + 1
{{1,4},{2,3},{5}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1 = 0 + 1
{{1,5},{2,3},{4}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1 = 0 + 1
{{1},{2,3},{4,5}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1 = 0 + 1
{{1,4},{2,5},{3}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1 = 0 + 1
{{1,5},{2,4},{3}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1 = 0 + 1
{{1},{2,4},{3,5}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1 = 0 + 1
{{1},{2,5},{3,4}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1 = 0 + 1
{{1,2,3},{4,5,6}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 1
{{1,2,3},{4,5},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,2,3},{4,6},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,2,4},{3,5,6}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 1
{{1,2,4},{3,5},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,2,4},{3,6},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,2,5},{3,4,6}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 1
{{1,2,5},{3,4},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,2,6},{3,4,5}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 1
{{1,2},{3,4,5},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1 + 1
{{1,2,6},{3,4},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,2},{3,4,6},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1 + 1
{{1,2},{3,4},{5,6}}
 => [2,2,2]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 1
{{1,2},{3,4},{5},{6}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,2,5},{3,6},{4}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,2,6},{3,5},{4}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,2},{3,5,6},{4}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1 + 1
{{1,2},{3,5},{4,6}}
 => [2,2,2]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 1
{{1,2},{3,5},{4},{6}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,2},{3,6},{4,5}}
 => [2,2,2]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 1
{{1,2},{3},{4,5},{6}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 1
{{1,2},{3,6},{4},{5}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,2},{3},{4,6},{5}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 1
{{1,3,4},{2,5,6}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 1
{{1,3,4},{2,5},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,3,4},{2,6},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,3,5},{2,4,6}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 1
{{1,3,5},{2,4},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,3,6},{2,4,5}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 1
{{1,3},{2,4,5},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1 + 1
{{1,3,6},{2,4},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,3},{2,4,6},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1 + 1
{{1,3},{2,4},{5,6}}
 => [2,2,2]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 1
{{1,3},{2,4},{5},{6}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,3,5},{2,6},{4}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,3,6},{2,5},{4}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,3},{2,5,6},{4}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1 + 1
{{1,3},{2,5},{4,6}}
 => [2,2,2]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 1
{{1,3},{2,5},{4},{6}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,3},{2,6},{4,5}}
 => [2,2,2]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 1
{{1,3},{2},{4,5},{6}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 1
{{1,3},{2,6},{4},{5}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,3},{2},{4,6},{5}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 1
{{1,4,5},{2,3,6}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 1
{{1,4,5},{2,3},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,4,6},{2,3,5}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 1
{{1,4},{2,3,5},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1 + 1
{{1,4,6},{2,3},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 1
{{1,4},{2,3,6},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1 + 1
{{1,4},{2,3},{5,6}}
 => [2,2,2]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 1
{{1,2,3,4},{5,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,2,3,5},{4,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,2,3,6},{4,5,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,2,3,7},{4,5,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,2,3},{4,5,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,2,4,5},{3,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,2,4,6},{3,5,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,2,4,7},{3,5,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,2,4},{3,5,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,2,5,6},{3,4,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,2,5,7},{3,4,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,2,5},{3,4,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,2,6,7},{3,4,5}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,2,6},{3,4,5,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,2,7},{3,4,5,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,3,4,5},{2,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,3,4,6},{2,5,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,3,4,7},{2,5,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,3,4},{2,5,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,3,5,6},{2,4,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,3,5,7},{2,4,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,3,5},{2,4,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,3,6,7},{2,4,5}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,3,6},{2,4,5,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,3,7},{2,4,5,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,4,5,6},{2,3,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,4,5,7},{2,3,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,4,5},{2,3,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,4,6,7},{2,3,5}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,4,6},{2,3,5,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,4,7},{2,3,5,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,5,6,7},{2,3,4}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,5,6},{2,3,4,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,5,7},{2,3,4,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1,6,7},{2,3,4,5}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
{{1},{2},{3,4,5},{6},{7}}
 => [3,1,1,1,1]
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => 1 = 0 + 1
{{1},{2},{3,4,6},{5},{7}}
 => [3,1,1,1,1]
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => 1 = 0 + 1
{{1},{2},{3,4,7},{5},{6}}
 => [3,1,1,1,1]
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => 1 = 0 + 1
{{1},{2},{3,5,6},{4},{7}}
 => [3,1,1,1,1]
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => 1 = 0 + 1

Description

The global dimension of the algebra

$A/AfA$ of the corresponding Nakayama algebra

$A$ with minimal left faithful projective-injective module

$Af$ .

Matching statistic: St001515
(load all 2 compositions to match this statistic)

Mapping

Mp00079: Set partitions —shape⟶ Integer partitions
Mp00312: Integer partitions —Glaisher-Franklin⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001515: Dyck paths ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 25%

Values

{{1,2},{3,4},{5}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 4 = 0 + 4
{{1,2},{3,5},{4}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 4 = 0 + 4
{{1,3},{2,4},{5}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 4 = 0 + 4
{{1,3},{2,5},{4}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 4 = 0 + 4
{{1,4},{2,3},{5}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 4 = 0 + 4
{{1,5},{2,3},{4}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 4 = 0 + 4
{{1},{2,3},{4,5}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 4 = 0 + 4
{{1,4},{2,5},{3}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 4 = 0 + 4
{{1,5},{2,4},{3}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 4 = 0 + 4
{{1},{2,4},{3,5}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 4 = 0 + 4
{{1},{2,5},{3,4}}
 => [2,2,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 4 = 0 + 4
{{1,2,3},{4,5,6}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 4
{{1,2,3},{4,5},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,2,3},{4,6},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,2,4},{3,5,6}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 4
{{1,2,4},{3,5},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,2,4},{3,6},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,2,5},{3,4,6}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 4
{{1,2,5},{3,4},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,2,6},{3,4,5}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 4
{{1,2},{3,4,5},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1 + 4
{{1,2,6},{3,4},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,2},{3,4,6},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1 + 4
{{1,2},{3,4},{5,6}}
 => [2,2,2]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 4
{{1,2},{3,4},{5},{6}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,2,5},{3,6},{4}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,2,6},{3,5},{4}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,2},{3,5,6},{4}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1 + 4
{{1,2},{3,5},{4,6}}
 => [2,2,2]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 4
{{1,2},{3,5},{4},{6}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,2},{3,6},{4,5}}
 => [2,2,2]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 4
{{1,2},{3},{4,5},{6}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 4
{{1,2},{3,6},{4},{5}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,2},{3},{4,6},{5}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 4
{{1,3,4},{2,5,6}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 4
{{1,3,4},{2,5},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,3,4},{2,6},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,3,5},{2,4,6}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 4
{{1,3,5},{2,4},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,3,6},{2,4,5}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 4
{{1,3},{2,4,5},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1 + 4
{{1,3,6},{2,4},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,3},{2,4,6},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1 + 4
{{1,3},{2,4},{5,6}}
 => [2,2,2]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 4
{{1,3},{2,4},{5},{6}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,3,5},{2,6},{4}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,3,6},{2,5},{4}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,3},{2,5,6},{4}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1 + 4
{{1,3},{2,5},{4,6}}
 => [2,2,2]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 4
{{1,3},{2,5},{4},{6}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,3},{2,6},{4,5}}
 => [2,2,2]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 4
{{1,3},{2},{4,5},{6}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 4
{{1,3},{2,6},{4},{5}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,3},{2},{4,6},{5}}
 => [2,2,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 4
{{1,4,5},{2,3,6}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 4
{{1,4,5},{2,3},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,4,6},{2,3,5}}
 => [3,3]
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 4
{{1,4},{2,3,5},{6}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1 + 4
{{1,4,6},{2,3},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 0 + 4
{{1,4},{2,3,6},{5}}
 => [3,2,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1 + 4
{{1,4},{2,3},{5,6}}
 => [2,2,2]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 4
{{1,2,3,4},{5,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,2,3,5},{4,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,2,3,6},{4,5,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,2,3,7},{4,5,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,2,3},{4,5,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,2,4,5},{3,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,2,4,6},{3,5,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,2,4,7},{3,5,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,2,4},{3,5,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,2,5,6},{3,4,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,2,5,7},{3,4,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,2,5},{3,4,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,2,6,7},{3,4,5}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,2,6},{3,4,5,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,2,7},{3,4,5,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,3,4,5},{2,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,3,4,6},{2,5,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,3,4,7},{2,5,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,3,4},{2,5,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,3,5,6},{2,4,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,3,5,7},{2,4,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,3,5},{2,4,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,3,6,7},{2,4,5}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,3,6},{2,4,5,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,3,7},{2,4,5,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,4,5,6},{2,3,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,4,5,7},{2,3,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,4,5},{2,3,6,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,4,6,7},{2,3,5}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,4,6},{2,3,5,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,4,7},{2,3,5,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,5,6,7},{2,3,4}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,5,6},{2,3,4,7}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,5,7},{2,3,4,6}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1,6,7},{2,3,4,5}}
 => [4,3]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4 = 0 + 4
{{1},{2},{3,4,5},{6},{7}}
 => [3,1,1,1,1]
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => 4 = 0 + 4
{{1},{2},{3,4,6},{5},{7}}
 => [3,1,1,1,1]
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => 4 = 0 + 4
{{1},{2},{3,4,7},{5},{6}}
 => [3,1,1,1,1]
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => 4 = 0 + 4
{{1},{2},{3,5,6},{4},{7}}
 => [3,1,1,1,1]
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => 4 = 0 + 4

Description

The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule).

Matching statistic: St000455
(load all 8 compositions to match this statistic)

Mapping

Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000455: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 25%

Values

{{1,2},{3,4},{5}}
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0
{{1,2},{3,5},{4}}
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0
{{1,3},{2,4},{5}}
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0
{{1,3},{2,5},{4}}
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0
{{1,4},{2,3},{5}}
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0
{{1,5},{2,3},{4}}
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0
{{1},{2,3},{4,5}}
 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0
{{1,4},{2,5},{3}}
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0
{{1,5},{2,4},{3}}
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0
{{1},{2,4},{3,5}}
 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0
{{1},{2,5},{3,4}}
 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0
{{1,2,3},{4,5,6}}
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => 0
{{1,2,3},{4,5},{6}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,2,3},{4,6},{5}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,2,4},{3,5,6}}
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => 0
{{1,2,4},{3,5},{6}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,2,4},{3,6},{5}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,2,5},{3,4,6}}
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => 0
{{1,2,5},{3,4},{6}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,2,6},{3,4,5}}
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => 0
{{1,2},{3,4,5},{6}}
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
{{1,2,6},{3,4},{5}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,2},{3,4,6},{5}}
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
{{1,2},{3,4},{5,6}}
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
{{1,2},{3,4},{5},{6}}
 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,2,5},{3,6},{4}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,2,6},{3,5},{4}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,2},{3,5,6},{4}}
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
{{1,2},{3,5},{4,6}}
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
{{1,2},{3,5},{4},{6}}
 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,2},{3,6},{4,5}}
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
{{1,2},{3},{4,5},{6}}
 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
{{1,2},{3,6},{4},{5}}
 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,2},{3},{4,6},{5}}
 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
{{1,3,4},{2,5,6}}
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => 0
{{1,3,4},{2,5},{6}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,3,4},{2,6},{5}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,3,5},{2,4,6}}
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => 0
{{1,3,5},{2,4},{6}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,3,6},{2,4,5}}
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => 0
{{1,3},{2,4,5},{6}}
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
{{1,3,6},{2,4},{5}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,3},{2,4,6},{5}}
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
{{1,3},{2,4},{5,6}}
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
{{1,3},{2,4},{5},{6}}
 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,3,5},{2,6},{4}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,3,6},{2,5},{4}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,3},{2,5,6},{4}}
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
{{1,3},{2,5},{4,6}}
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
{{1,3},{2,5},{4},{6}}
 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,3},{2,6},{4,5}}
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
{{1,3},{2},{4,5},{6}}
 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
{{1,3},{2,6},{4},{5}}
 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,3},{2},{4,6},{5}}
 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
{{1,4,5},{2,3,6}}
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => 0
{{1,4,5},{2,3},{6}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,4,6},{2,3,5}}
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => 0
{{1,4},{2,3,5},{6}}
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1
{{1,4,6},{2,3},{5}}
 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0
{{1,5,6},{2,3,4}}
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => 0
{{1,2,3,4},{5,6,7}}
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 0
{{1,2,3,5},{4,6,7}}
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 0
{{1,2,3,6},{4,5,7}}
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 0
{{1,2,3,7},{4,5,6}}
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 0
{{1,2,3},{4,5,6,7}}
 => [3,4] => ([(3,6),(4,6),(5,6)],7)
 => 0
{{1,2,3},{4},{5,6,7}}
 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 0
{{1,2,4,5},{3,6,7}}
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 0
{{1,2,4,6},{3,5,7}}
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 0
{{1,2,4,7},{3,5,6}}
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 0
{{1,2,4},{3,5,6,7}}
 => [3,4] => ([(3,6),(4,6),(5,6)],7)
 => 0
{{1,2,4},{3},{5,6,7}}
 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 0
{{1,2,5,6},{3,4,7}}
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 0
{{1,2,5,7},{3,4,6}}
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 0
{{1,2,5},{3,4,6,7}}
 => [3,4] => ([(3,6),(4,6),(5,6)],7)
 => 0
{{1,2,6,7},{3,4,5}}
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 0
{{1,2,6},{3,4,5,7}}
 => [3,4] => ([(3,6),(4,6),(5,6)],7)
 => 0
{{1,2,7},{3,4,5,6}}
 => [3,4] => ([(3,6),(4,6),(5,6)],7)
 => 0
{{1,2,5},{3},{4,6,7}}
 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 0
{{1,2,6},{3},{4,5,7}}
 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 0
{{1,2,7},{3},{4,5,6}}
 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 0
{{1,3,4,5},{2,6,7}}
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 0
{{1,3,4,6},{2,5,7}}
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 0
{{1,3,4,7},{2,5,6}}
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 0
{{1,3,4},{2,5,6,7}}
 => [3,4] => ([(3,6),(4,6),(5,6)],7)
 => 0
{{1,3,4},{2},{5,6,7}}
 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 0
{{1,3,5,6},{2,4,7}}
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 0
{{1,3,5,7},{2,4,6}}
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 0
{{1,3,5},{2,4,6,7}}
 => [3,4] => ([(3,6),(4,6),(5,6)],7)
 => 0
{{1,3,6,7},{2,4,5}}
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 0
{{1,3,6},{2,4,5,7}}
 => [3,4] => ([(3,6),(4,6),(5,6)],7)
 => 0
{{1,3,7},{2,4,5,6}}
 => [3,4] => ([(3,6),(4,6),(5,6)],7)
 => 0
{{1,3,5},{2},{4,6,7}}
 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 0
{{1,3,6},{2},{4,5,7}}
 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 0
{{1,3,7},{2},{4,5,6}}
 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 0
{{1,4,5,6},{2,3,7}}
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 0
{{1,4,5,7},{2,3,6}}
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 0
{{1,4,5},{2,3,6,7}}
 => [3,4] => ([(3,6),(4,6),(5,6)],7)
 => 0
{{1,4,6,7},{2,3,5}}
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => 0
{{1,4,6},{2,3,5,7}}
 => [3,4] => ([(3,6),(4,6),(5,6)],7)
 => 0
{{1,4,7},{2,3,5,6}}
 => [3,4] => ([(3,6),(4,6),(5,6)],7)
 => 0

Description

The second largest eigenvalue of a graph if it is integral. This statistic is undefined if the second largest eigenvalue of the graph is not integral. Chapter 4 of [1] provides lots of context.

Matching statistic: St001645
(load all 9 compositions to match this statistic)

Mapping

Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 25%

Values

{{1,2},{3,4},{5}}
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 7
{{1,2},{3,5},{4}}
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 7
{{1,3},{2,4},{5}}
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 7
{{1,3},{2,5},{4}}
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 7
{{1,4},{2,3},{5}}
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 7
{{1,5},{2,3},{4}}
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 7
{{1},{2,3},{4,5}}
 => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 7
{{1,4},{2,5},{3}}
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 7
{{1,5},{2,4},{3}}
 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 7
{{1},{2,4},{3,5}}
 => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 7
{{1},{2,5},{3,4}}
 => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 7
{{1,2,3},{4,5,6}}
 => [3,3] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,2,3},{4,5},{6}}
 => [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,2,3},{4,6},{5}}
 => [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,2,4},{3,5,6}}
 => [3,3] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,2,4},{3,5},{6}}
 => [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,2,4},{3,6},{5}}
 => [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,2,5},{3,4,6}}
 => [3,3] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,2,5},{3,4},{6}}
 => [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,2,6},{3,4,5}}
 => [3,3] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,2},{3,4,5},{6}}
 => [2,3,1] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 7
{{1,2,6},{3,4},{5}}
 => [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,2},{3,4,6},{5}}
 => [2,3,1] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 7
{{1,2},{3,4},{5,6}}
 => [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 7
{{1,2},{3,4},{5},{6}}
 => [2,2,1,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,2,5},{3,6},{4}}
 => [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,2,6},{3,5},{4}}
 => [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,2},{3,5,6},{4}}
 => [2,3,1] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 7
{{1,2},{3,5},{4,6}}
 => [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 7
{{1,2},{3,5},{4},{6}}
 => [2,2,1,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,2},{3,6},{4,5}}
 => [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 7
{{1,2},{3},{4,5},{6}}
 => [2,1,2,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 7
{{1,2},{3,6},{4},{5}}
 => [2,2,1,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,2},{3},{4,6},{5}}
 => [2,1,2,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 7
{{1,3,4},{2,5,6}}
 => [3,3] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,3,4},{2,5},{6}}
 => [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,3,4},{2,6},{5}}
 => [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,3,5},{2,4,6}}
 => [3,3] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,3,5},{2,4},{6}}
 => [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,3,6},{2,4,5}}
 => [3,3] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,3},{2,4,5},{6}}
 => [2,3,1] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 7
{{1,3,6},{2,4},{5}}
 => [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,3},{2,4,6},{5}}
 => [2,3,1] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 7
{{1,3},{2,4},{5,6}}
 => [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 7
{{1,3},{2,4},{5},{6}}
 => [2,2,1,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,3,5},{2,6},{4}}
 => [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,3,6},{2,5},{4}}
 => [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,3},{2,5,6},{4}}
 => [2,3,1] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 7
{{1,3},{2,5},{4,6}}
 => [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 7
{{1,3},{2,5},{4},{6}}
 => [2,2,1,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 7
{{1,2,3,4},{5,6,7}}
 => [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,3,4},{5,6},{7}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,3,4},{5,7},{6}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,3,5},{4,6,7}}
 => [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,3,5},{4,6},{7}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,3,5},{4,7},{6}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,3,6},{4,5,7}}
 => [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,3,6},{4,5},{7}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,3,7},{4,5,6}}
 => [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,3,7},{4,5},{6}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,3,6},{4,7},{5}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,3,7},{4,6},{5}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,4,5},{3,6,7}}
 => [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,4,5},{3,6},{7}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,4,5},{3,7},{6}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,4,6},{3,5,7}}
 => [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,4,6},{3,5},{7}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,4,7},{3,5,6}}
 => [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,4,7},{3,5},{6}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,4,6},{3,7},{5}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,4,7},{3,6},{5}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,5,6},{3,4,7}}
 => [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,5,6},{3,4},{7}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,5,7},{3,4,6}}
 => [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,5,7},{3,4},{6}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,6,7},{3,4,5}}
 => [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,6,7},{3,4},{5}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,5,6},{3,7},{4}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,5,7},{3,6},{4}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,2,6,7},{3,5},{4}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,3,4,5},{2,6,7}}
 => [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,3,4,5},{2,6},{7}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,3,4,5},{2,7},{6}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,3,4,6},{2,5,7}}
 => [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,3,4,6},{2,5},{7}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,3,4,7},{2,5,6}}
 => [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,3,4,7},{2,5},{6}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,3,4,6},{2,7},{5}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,3,4,7},{2,6},{5}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,3,5,6},{2,4,7}}
 => [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,3,5,6},{2,4},{7}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,3,5,7},{2,4,6}}
 => [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,3,5,7},{2,4},{6}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,3,6,7},{2,4,5}}
 => [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,3,6,7},{2,4},{5}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,3,5,6},{2,7},{4}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,3,5,7},{2,6},{4}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,3,6,7},{2,5},{4}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,4,5,6},{2,3,7}}
 => [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7
{{1,4,5,6},{2,3},{7}}
 => [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 0 + 7

Description

The pebbling number of a connected graph.

Matching statistic: St001964

Mapping

Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St001964: Posets ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 25%

Values

{{1,2},{3,4},{5}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 0
{{1,2},{3,5},{4}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 0
{{1,3},{2,4},{5}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 0
{{1,3},{2,5},{4}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 0
{{1,4},{2,3},{5}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 0
{{1,5},{2,3},{4}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 0
{{1},{2,3},{4,5}}
 => [1,2,2] => [[3,2,1],[1]]
 => ([(0,3),(0,4),(1,2),(1,4)],5)
 => 0
{{1,4},{2,5},{3}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 0
{{1,5},{2,4},{3}}
 => [2,2,1] => [[3,3,2],[2,1]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 0
{{1},{2,4},{3,5}}
 => [1,2,2] => [[3,2,1],[1]]
 => ([(0,3),(0,4),(1,2),(1,4)],5)
 => 0
{{1},{2,5},{3,4}}
 => [1,2,2] => [[3,2,1],[1]]
 => ([(0,3),(0,4),(1,2),(1,4)],5)
 => 0
{{1,2,3},{4,5,6}}
 => [3,3] => [[5,3],[2]]
 => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ? = 0
{{1,2,3},{4,5},{6}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,2,3},{4,6},{5}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,2,4},{3,5,6}}
 => [3,3] => [[5,3],[2]]
 => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ? = 0
{{1,2,4},{3,5},{6}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,2,4},{3,6},{5}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,2,5},{3,4,6}}
 => [3,3] => [[5,3],[2]]
 => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ? = 0
{{1,2,5},{3,4},{6}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,2,6},{3,4,5}}
 => [3,3] => [[5,3],[2]]
 => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ? = 0
{{1,2},{3,4,5},{6}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1
{{1,2,6},{3,4},{5}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,2},{3,4,6},{5}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1
{{1,2},{3,4},{5,6}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ? = 1
{{1,2},{3,4},{5},{6}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,2,5},{3,6},{4}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,2,6},{3,5},{4}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,2},{3,5,6},{4}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1
{{1,2},{3,5},{4,6}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ? = 1
{{1,2},{3,5},{4},{6}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,2},{3,6},{4,5}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ? = 1
{{1,2},{3},{4,5},{6}}
 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1
{{1,2},{3,6},{4},{5}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,2},{3},{4,6},{5}}
 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1
{{1,3,4},{2,5,6}}
 => [3,3] => [[5,3],[2]]
 => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ? = 0
{{1,3,4},{2,5},{6}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,3,4},{2,6},{5}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,3,5},{2,4,6}}
 => [3,3] => [[5,3],[2]]
 => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ? = 0
{{1,3,5},{2,4},{6}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,3,6},{2,4,5}}
 => [3,3] => [[5,3],[2]]
 => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ? = 0
{{1,3},{2,4,5},{6}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1
{{1,3,6},{2,4},{5}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,3},{2,4,6},{5}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1
{{1,3},{2,4},{5,6}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ? = 1
{{1,3},{2,4},{5},{6}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,3,5},{2,6},{4}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,3,6},{2,5},{4}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,3},{2,5,6},{4}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1
{{1,3},{2,5},{4,6}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ? = 1
{{1,3},{2,5},{4},{6}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,3},{2,6},{4,5}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ? = 1
{{1,3},{2},{4,5},{6}}
 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1
{{1,3},{2,6},{4},{5}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,3},{2},{4,6},{5}}
 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1
{{1,4,5},{2,3,6}}
 => [3,3] => [[5,3],[2]]
 => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ? = 0
{{1,4,5},{2,3},{6}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,4,6},{2,3,5}}
 => [3,3] => [[5,3],[2]]
 => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ? = 0
{{1,4},{2,3,5},{6}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1
{{1,4,6},{2,3},{5}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,4},{2,3,6},{5}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1
{{1,4},{2,3},{5,6}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ? = 1
{{1,4},{2,3},{5},{6}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,5,6},{2,3,4}}
 => [3,3] => [[5,3],[2]]
 => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
 => ? = 0
{{1,5},{2,3,4},{6}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1
{{1,6},{2,3,4},{5}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1
{{1},{2,3,4},{5,6}}
 => [1,3,2] => [[4,3,1],[2]]
 => ([(0,4),(0,5),(1,2),(1,3),(3,5)],6)
 => ? = 1
{{1,5,6},{2,3},{4}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,5},{2,3,6},{4}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1
{{1,5},{2,3},{4,6}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ? = 1
{{1,5},{2,3},{4},{6}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,6},{2,3,5},{4}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1
{{1},{2,3,5},{4,6}}
 => [1,3,2] => [[4,3,1],[2]]
 => ([(0,4),(0,5),(1,2),(1,3),(3,5)],6)
 => ? = 1
{{1,6},{2,3},{4,5}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ? = 1
{{1},{2,3,6},{4,5}}
 => [1,3,2] => [[4,3,1],[2]]
 => ([(0,4),(0,5),(1,2),(1,3),(3,5)],6)
 => ? = 1
{{1},{2,3},{4,5,6}}
 => [1,2,3] => [[4,2,1],[1]]
 => ([(0,3),(0,5),(1,4),(1,5),(4,2)],6)
 => ? = 0
{{1},{2,3},{4,5},{6}}
 => [1,2,2,1] => [[3,3,2,1],[2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ? = 1
{{1,6},{2,3},{4},{5}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1},{2,3},{4,6},{5}}
 => [1,2,2,1] => [[3,3,2,1],[2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ? = 1
{{1},{2,3},{4},{5,6}}
 => [1,2,1,2] => [[3,2,2,1],[1,1]]
 => ([(0,4),(0,5),(1,2),(1,3),(3,5)],6)
 => ? = 1
{{1,4,5},{2,6},{3}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,4,6},{2,5},{3}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,4},{2,5,6},{3}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1
{{1,4},{2,5},{3,6}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ? = 1
{{1,4},{2,5},{3},{6}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,4},{2,6},{3,5}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ? = 1
{{1,4},{2},{3,5},{6}}
 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1
{{1,4},{2,6},{3},{5}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,4},{2},{3,6},{5}}
 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1
{{1,5,6},{2,4},{3}}
 => [3,2,1] => [[4,4,3],[3,2]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,5},{2,4,6},{3}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1
{{1,5},{2,4},{3,6}}
 => [2,2,2] => [[4,3,2],[2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ? = 1
{{1,5},{2,4},{3},{6}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,6},{2,4,5},{3}}
 => [2,3,1] => [[4,4,2],[3,1]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1
{{1,6},{2,4},{3},{5}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,5},{2,6},{3},{4}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0
{{1,6},{2,5},{3},{4}}
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => 0

Description

The interval resolution global dimension of a poset. This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.

Matching statistic: St001803

Mapping

Mp00079: Set partitions —shape⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
St001803: Standard tableaux ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 50%

Values

{{1,2},{3,4},{5}}
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [[1,2,3,6],[4,5,7,8]]
 => 0
{{1,2},{3,5},{4}}
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [[1,2,3,6],[4,5,7,8]]
 => 0
{{1,3},{2,4},{5}}
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [[1,2,3,6],[4,5,7,8]]
 => 0
{{1,3},{2,5},{4}}
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [[1,2,3,6],[4,5,7,8]]
 => 0
{{1,4},{2,3},{5}}
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [[1,2,3,6],[4,5,7,8]]
 => 0
{{1,5},{2,3},{4}}
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [[1,2,3,6],[4,5,7,8]]
 => 0
{{1},{2,3},{4,5}}
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [[1,2,3,6],[4,5,7,8]]
 => 0
{{1,4},{2,5},{3}}
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [[1,2,3,6],[4,5,7,8]]
 => 0
{{1,5},{2,4},{3}}
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [[1,2,3,6],[4,5,7,8]]
 => 0
{{1},{2,4},{3,5}}
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [[1,2,3,6],[4,5,7,8]]
 => 0
{{1},{2,5},{3,4}}
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [[1,2,3,6],[4,5,7,8]]
 => 0
{{1,2,3},{4,5,6}}
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [[1,2,3,5],[4,6,7,8]]
 => 0
{{1,2,3},{4,5},{6}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 0
{{1,2,3},{4,6},{5}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 0
{{1,2,4},{3,5,6}}
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [[1,2,3,5],[4,6,7,8]]
 => 0
{{1,2,4},{3,5},{6}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 0
{{1,2,4},{3,6},{5}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 0
{{1,2,5},{3,4,6}}
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [[1,2,3,5],[4,6,7,8]]
 => 0
{{1,2,5},{3,4},{6}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 0
{{1,2,6},{3,4,5}}
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [[1,2,3,5],[4,6,7,8]]
 => 0
{{1,2},{3,4,5},{6}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 1
{{1,2,6},{3,4},{5}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 0
{{1,2},{3,4,6},{5}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 1
{{1,2},{3,4},{5,6}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [[1,2,3,4],[5,6,7,8]]
 => 1
{{1,2},{3,4},{5},{6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[1,2,3,6,8],[4,5,7,9,10]]
 => ? = 0
{{1,2,5},{3,6},{4}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 0
{{1,2,6},{3,5},{4}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 0
{{1,2},{3,5,6},{4}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 1
{{1,2},{3,5},{4,6}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [[1,2,3,4],[5,6,7,8]]
 => 1
{{1,2},{3,5},{4},{6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[1,2,3,6,8],[4,5,7,9,10]]
 => ? = 0
{{1,2},{3,6},{4,5}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [[1,2,3,4],[5,6,7,8]]
 => 1
{{1,2},{3},{4,5},{6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[1,2,3,6,8],[4,5,7,9,10]]
 => ? = 1
{{1,2},{3,6},{4},{5}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[1,2,3,6,8],[4,5,7,9,10]]
 => ? = 0
{{1,2},{3},{4,6},{5}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[1,2,3,6,8],[4,5,7,9,10]]
 => ? = 1
{{1,3,4},{2,5,6}}
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [[1,2,3,5],[4,6,7,8]]
 => 0
{{1,3,4},{2,5},{6}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 0
{{1,3,4},{2,6},{5}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 0
{{1,3,5},{2,4,6}}
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [[1,2,3,5],[4,6,7,8]]
 => 0
{{1,3,5},{2,4},{6}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 0
{{1,3,6},{2,4,5}}
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [[1,2,3,5],[4,6,7,8]]
 => 0
{{1,3},{2,4,5},{6}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 1
{{1,3,6},{2,4},{5}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 0
{{1,3},{2,4,6},{5}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 1
{{1,3},{2,4},{5,6}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [[1,2,3,4],[5,6,7,8]]
 => 1
{{1,3},{2,4},{5},{6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[1,2,3,6,8],[4,5,7,9,10]]
 => ? = 0
{{1,3,5},{2,6},{4}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 0
{{1,3,6},{2,5},{4}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 0
{{1,3},{2,5,6},{4}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 1
{{1,3},{2,5},{4,6}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [[1,2,3,4],[5,6,7,8]]
 => 1
{{1,3},{2,5},{4},{6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[1,2,3,6,8],[4,5,7,9,10]]
 => ? = 0
{{1,3},{2,6},{4,5}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [[1,2,3,4],[5,6,7,8]]
 => 1
{{1,3},{2},{4,5},{6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[1,2,3,6,8],[4,5,7,9,10]]
 => ? = 1
{{1,3},{2,6},{4},{5}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[1,2,3,6,8],[4,5,7,9,10]]
 => ? = 0
{{1,3},{2},{4,6},{5}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[1,2,3,6,8],[4,5,7,9,10]]
 => ? = 1
{{1,4,5},{2,3,6}}
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [[1,2,3,5],[4,6,7,8]]
 => 0
{{1,4,5},{2,3},{6}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 0
{{1,4,6},{2,3,5}}
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [[1,2,3,5],[4,6,7,8]]
 => 0
{{1,4},{2,3,5},{6}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 1
{{1,4,6},{2,3},{5}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 0
{{1,4},{2,3,6},{5}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 1
{{1,4},{2,3},{5,6}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [[1,2,3,4],[5,6,7,8]]
 => 1
{{1,4},{2,3},{5},{6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[1,2,3,6,8],[4,5,7,9,10]]
 => ? = 0
{{1,5,6},{2,3,4}}
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [[1,2,3,5],[4,6,7,8]]
 => 0
{{1,5},{2,3,4},{6}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 1
{{1,6},{2,3,4},{5}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 1
{{1},{2,3,4},{5,6}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 1
{{1,5,6},{2,3},{4}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 0
{{1,5},{2,3,6},{4}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 1
{{1,5},{2,3},{4,6}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [[1,2,3,4],[5,6,7,8]]
 => 1
{{1,5},{2,3},{4},{6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[1,2,3,6,8],[4,5,7,9,10]]
 => ? = 0
{{1,6},{2,3,5},{4}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 1
{{1},{2,3,5},{4,6}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 1
{{1,6},{2,3},{4,5}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [[1,2,3,4],[5,6,7,8]]
 => 1
{{1},{2,3,6},{4,5}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 1
{{1},{2,3},{4,5,6}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 0
{{1},{2,3},{4,5},{6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[1,2,3,6,8],[4,5,7,9,10]]
 => ? = 1
{{1,6},{2,3},{4},{5}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[1,2,3,6,8],[4,5,7,9,10]]
 => ? = 0
{{1},{2,3},{4,6},{5}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[1,2,3,6,8],[4,5,7,9,10]]
 => ? = 1
{{1},{2,3},{4},{5,6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[1,2,3,6,8],[4,5,7,9,10]]
 => ? = 1
{{1,4,5},{2,6},{3}}
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [[1,3,4,5,8],[2,6,7,9,10]]
 => ? = 0
{{1,4},{2,5},{3,6}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [[1,2,3,4],[5,6,7,8]]
 => 1
{{1,4},{2,6},{3,5}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [[1,2,3,4],[5,6,7,8]]
 => 1
{{1,5},{2,4},{3,6}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [[1,2,3,4],[5,6,7,8]]
 => 1
{{1,6},{2,4},{3,5}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [[1,2,3,4],[5,6,7,8]]
 => 1
{{1,5},{2,6},{3,4}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [[1,2,3,4],[5,6,7,8]]
 => 1
{{1,6},{2,5},{3,4}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [[1,2,3,4],[5,6,7,8]]
 => 1

Description

The maximal overlap of the cylindrical tableau associated with a tableau. A cylindrical tableau associated with a standard Young tableau

$T$ is the skew row-strict tableau obtained by gluing two copies of

$T$ such that the inner shape is a rectangle. The overlap, recorded in this statistic, equals

$\max_C\big(2\ell(T) - \ell(C)\big)$ , where

$\ell$ denotes the number of rows of a tableau and the maximum is taken over all cylindrical tableaux. In particular, the statistic equals

$0$ , if and only if the last entry of the first row is larger than or equal to the first entry of the last row. Moreover, the statistic attains its maximal value, the number of rows of the tableau minus 1, if and only if the tableau consists of a single column.

The following 17 statistics, ordered by result quality, also match your data. Click on any of them to see the details.

St001413Half the length of the longest even length palindromic prefix of a binary word. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001415The length of the longest palindromic prefix of a binary word. St001424The number of distinct squares in a binary word. St000393The number of strictly increasing runs in a binary word. St000356The number of occurrences of the pattern 13-2. St001083The number of boxed occurrences of 132 in a permutation. St000483The number of times a permutation switches from increasing to decreasing or decreasing to increasing. St000672The number of minimal elements in Bruhat order not less than the permutation. St000018The number of inversions of a permutation. St000019The cardinality of the support of a permutation. St000670The reversal length of a permutation. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001200The number of simple modules in

$eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra

$A$ with minimal faithful projective-injective module

$eA$ . St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition.