searching the database
Your data matches 5 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St001877
Mp00102: Dyck paths —rise 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%
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
[1,0,1,1,0,0,1,1,0,0]
=> [1,2,2] => [[3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,1,0,1,1,0,0,0]
=> [1,2,2] => [[3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,0,1,1,0,0,1,0]
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,0,1,1,0,1,0,0]
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,0,0,1,0]
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,0,1,0,0]
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,1,0,0,0]
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,2,1,1] => [[2,2,2,1,1],[1,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,2,2] => [[3,2,1,1],[1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,2,1,1] => [[2,2,2,1,1],[1,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,2,1,1] => [[2,2,2,1,1],[1,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,2,2] => [[3,2,1,1],[1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,2,1,2] => [[3,2,2,1],[1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,2,2,1] => [[3,3,2,1],[2,1]]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,2,2,1] => [[3,3,2,1],[2,1]]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,2,3] => [[4,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,2,1,2] => [[3,2,2,1],[1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,2,1,2] => [[3,2,2,1],[1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,2,2,1] => [[3,3,2,1],[2,1]]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,2,2,1] => [[3,3,2,1],[2,1]]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,2,2,1] => [[3,3,2,1],[2,1]]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,2,3] => [[4,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,3,2] => [[4,3,1],[2]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,3,2] => [[4,3,1],[2]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,3,2] => [[4,3,1],[2]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,0,1,0,1,1,0,1,0,0]
=> [2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [2,2,2] => [[4,3,2],[2,1]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,0,1,1,0,1,0,1,0,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [2,2,2] => [[4,3,2],[2,1]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [2,3,1] => [[4,4,2],[3,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [2,3,1] => [[4,4,2],[3,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,0,1,1,1,0,1,0,0,0]
=> [2,3,1] => [[4,4,2],[3,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,1,0,1,1,0,0,0,1,0]
=> [2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,1,1,0,0,0,1,0,1,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [2,2,2] => [[4,3,2],[2,1]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,2,2] => [[4,3,2],[2,1]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1
[1,1,0,1,1,0,1,0,0,0,1,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [2,2,2] => [[4,3,2],[2,1]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1
[1,1,0,1,1,1,0,0,0,0,1,0]
=> [2,3,1] => [[4,4,2],[3,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
Description
Number of indecomposable injective modules with projective dimension 2.
Matching statistic: St001876
Mp00102: Dyck paths —rise 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: 75%●distinct values known / distinct values provided: 75%
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001876: Lattices ⟶ ℤResult quality: 75% ●values known / values provided: 75%●distinct values known / distinct values provided: 75%
Values
[1,0,1,1,0,0,1,1,0,0]
=> [1,2,2] => [[3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,1,0,1,1,0,0,0]
=> [1,2,2] => [[3,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,0,1,1,0,0,1,0]
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,0,1,1,0,1,0,0]
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,0,0,1,0]
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,0,1,0,0]
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,1,0,0,0]
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,2,1,1] => [[2,2,2,1,1],[1,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,2,2] => [[3,2,1,1],[1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,2,1,1] => [[2,2,2,1,1],[1,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,2,1,1] => [[2,2,2,1,1],[1,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,2,2] => [[3,2,1,1],[1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,2,1,2] => [[3,2,2,1],[1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,2,2,1] => [[3,3,2,1],[2,1]]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,2,2,1] => [[3,3,2,1],[2,1]]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,2,3] => [[4,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,2,1,2] => [[3,2,2,1],[1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,2,1,2] => [[3,2,2,1],[1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,2,2,1] => [[3,3,2,1],[2,1]]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,2,2,1] => [[3,3,2,1],[2,1]]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,2,2,1] => [[3,3,2,1],[2,1]]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 1
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,2,3] => [[4,2,1],[1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,3,2] => [[4,3,1],[2]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,3,2] => [[4,3,1],[2]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,3,2] => [[4,3,1],[2]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,0,1,0,1,1,0,1,0,0]
=> [2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [2,2,2] => [[4,3,2],[2,1]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,0,1,1,0,1,0,1,0,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [2,2,2] => [[4,3,2],[2,1]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [2,3,1] => [[4,4,2],[3,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [2,3,1] => [[4,4,2],[3,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,0,1,1,1,0,1,0,0,0]
=> [2,3,1] => [[4,4,2],[3,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,1,0,1,1,0,0,0,1,0]
=> [2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,1,1,0,0,0,1,0,1,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [2,2,2] => [[4,3,2],[2,1]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,2,2] => [[4,3,2],[2,1]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1
[1,1,0,1,1,0,1,0,0,0,1,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [2,2,2] => [[4,3,2],[2,1]]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1
[1,1,0,1,1,1,0,0,0,0,1,0]
=> [2,3,1] => [[4,4,2],[3,1]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,2,2,2] => [[4,3,2,1],[2,1]]
=> ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> ? = 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,2,2,2] => [[4,3,2,1],[2,1]]
=> ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> ? = 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> [1,2,3,1] => [[4,4,2,1],[3,1]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ? = 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
=> [1,2,3,1] => [[4,4,2,1],[3,1]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ? = 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
=> [1,2,3,1] => [[4,4,2,1],[3,1]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ? = 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
=> [1,2,2,2] => [[4,3,2,1],[2,1]]
=> ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> ? = 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,2,2,2] => [[4,3,2,1],[2,1]]
=> ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> ? = 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,2,2,2] => [[4,3,2,1],[2,1]]
=> ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> ? = 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
=> [1,2,3,1] => [[4,4,2,1],[3,1]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ? = 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,2,3,1] => [[4,4,2,1],[3,1]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ? = 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,2,3,1] => [[4,4,2,1],[3,1]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ? = 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,2,3,1] => [[4,4,2,1],[3,1]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ? = 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
=> [1,3,1,2] => [[4,3,3,1],[2,2]]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ? = 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
=> [1,3,2,1] => [[4,4,3,1],[3,2]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ? = 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
=> [1,3,2,1] => [[4,4,3,1],[3,2]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ? = 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
=> [1,3,1,2] => [[4,3,3,1],[2,2]]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ? = 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,3,1,2] => [[4,3,3,1],[2,2]]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ? = 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
=> [1,3,2,1] => [[4,4,3,1],[3,2]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ? = 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,3,2,1] => [[4,4,3,1],[3,2]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ? = 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,3,2,1] => [[4,4,3,1],[3,2]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ? = 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
=> [1,3,1,2] => [[4,3,3,1],[2,2]]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ? = 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,3,1,2] => [[4,3,3,1],[2,2]]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ? = 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,3,1,2] => [[4,3,3,1],[2,2]]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ? = 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,3,2,1] => [[4,4,3,1],[3,2]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ? = 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,3,2,1] => [[4,4,3,1],[3,2]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ? = 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,3,2,1] => [[4,4,3,1],[3,2]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ? = 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,3,2,1] => [[4,4,3,1],[3,2]]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> ? = 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
=> [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
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
=> [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
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
=> [2,1,3,1] => [[4,4,2,2],[3,1,1]]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ? = 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
=> [2,1,3,1] => [[4,4,2,2],[3,1,1]]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ? = 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
=> [2,1,3,1] => [[4,4,2,2],[3,1,1]]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ? = 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
=> [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
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> [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
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
=> [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
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
=> [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
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
=> [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
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
=> [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
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
=> [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
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
=> [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
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
=> [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
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
=> [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
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
=> [2,1,3,1] => [[4,4,2,2],[3,1,1]]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ? = 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
=> [2,1,3,1] => [[4,4,2,2],[3,1,1]]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ? = 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
=> [2,1,3,1] => [[4,4,2,2],[3,1,1]]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ? = 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
=> [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
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
=> [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
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=> [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
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
=> [2,1,3,1] => [[4,4,2,2],[3,1,1]]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ? = 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
=> [2,1,3,1] => [[4,4,2,2],[3,1,1]]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ? = 2
Description
The number of 2-regular simple modules in the incidence algebra of the lattice.
Matching statistic: St001964
Mp00102: Dyck paths —rise 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%
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
[1,0,1,1,0,0,1,1,0,0]
=> [1,2,2] => [[3,2,1],[1]]
=> ([(0,3),(0,4),(1,2),(1,4)],5)
=> 0
[1,0,1,1,0,1,1,0,0,0]
=> [1,2,2] => [[3,2,1],[1]]
=> ([(0,3),(0,4),(1,2),(1,4)],5)
=> 0
[1,1,0,0,1,1,0,0,1,0]
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 0
[1,1,0,0,1,1,0,1,0,0]
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 0
[1,1,0,1,1,0,0,0,1,0]
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 0
[1,1,0,1,1,0,0,1,0,0]
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 0
[1,1,0,1,1,0,1,0,0,0]
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 0
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,2,1,1] => [[2,2,2,1,1],[1,1]]
=> ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ? = 0
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,2,2] => [[3,2,1,1],[1]]
=> ([(0,3),(0,5),(1,4),(1,5),(4,2)],6)
=> ? = 0
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,2,1,1] => [[2,2,2,1,1],[1,1]]
=> ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ? = 0
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,2,1,1] => [[2,2,2,1,1],[1,1]]
=> ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ? = 0
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,2,2] => [[3,2,1,1],[1]]
=> ([(0,3),(0,5),(1,4),(1,5),(4,2)],6)
=> ? = 0
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,2,1,2] => [[3,2,2,1],[1,1]]
=> ([(0,4),(0,5),(1,2),(1,3),(3,5)],6)
=> ? = 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,2,2,1] => [[3,3,2,1],[2,1]]
=> ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
=> ? = 1
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,2,2,1] => [[3,3,2,1],[2,1]]
=> ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
=> ? = 1
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,2,3] => [[4,2,1],[1]]
=> ([(0,3),(0,5),(1,4),(1,5),(4,2)],6)
=> ? = 0
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,2,1,2] => [[3,2,2,1],[1,1]]
=> ([(0,4),(0,5),(1,2),(1,3),(3,5)],6)
=> ? = 1
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,2,1,2] => [[3,2,2,1],[1,1]]
=> ([(0,4),(0,5),(1,2),(1,3),(3,5)],6)
=> ? = 1
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,2,2,1] => [[3,3,2,1],[2,1]]
=> ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
=> ? = 1
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,2,2,1] => [[3,3,2,1],[2,1]]
=> ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
=> ? = 1
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,2,2,1] => [[3,3,2,1],[2,1]]
=> ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
=> ? = 1
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,2,3] => [[4,2,1],[1]]
=> ([(0,3),(0,5),(1,4),(1,5),(4,2)],6)
=> ? = 0
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,3,2] => [[4,3,1],[2]]
=> ([(0,4),(0,5),(1,2),(1,3),(3,5)],6)
=> ? = 1
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,3,2] => [[4,3,1],[2]]
=> ([(0,4),(0,5),(1,2),(1,3),(3,5)],6)
=> ? = 1
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,3,2] => [[4,3,1],[2]]
=> ([(0,4),(0,5),(1,2),(1,3),(3,5)],6)
=> ? = 1
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ? = 1
[1,1,0,0,1,0,1,1,0,1,0,0]
=> [2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ? = 1
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
=> 0
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [2,2,2] => [[4,3,2],[2,1]]
=> ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
=> ? = 1
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
=> 0
[1,1,0,0,1,1,0,1,0,1,0,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
=> 0
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [2,2,2] => [[4,3,2],[2,1]]
=> ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
=> ? = 1
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [2,3,1] => [[4,4,2],[3,1]]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ? = 1
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [2,3,1] => [[4,4,2],[3,1]]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ? = 1
[1,1,0,0,1,1,1,0,1,0,0,0]
=> [2,3,1] => [[4,4,2],[3,1]]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ? = 1
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ? = 1
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ? = 1
[1,1,0,1,0,1,1,0,0,0,1,0]
=> [2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ? = 1
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ? = 1
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ? = 1
[1,1,0,1,1,0,0,0,1,0,1,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
=> 0
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [2,2,2] => [[4,3,2],[2,1]]
=> ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
=> ? = 1
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
=> 0
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
=> 0
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,2,2] => [[4,3,2],[2,1]]
=> ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
=> ? = 1
[1,1,0,1,1,0,1,0,0,0,1,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
=> 0
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
=> 0
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
=> 0
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [2,2,2] => [[4,3,2],[2,1]]
=> ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
=> ? = 1
[1,1,0,1,1,1,0,0,0,0,1,0]
=> [2,3,1] => [[4,4,2],[3,1]]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ? = 1
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [2,3,1] => [[4,4,2],[3,1]]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ? = 1
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [2,3,1] => [[4,4,2],[3,1]]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ? = 1
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [2,3,1] => [[4,4,2],[3,1]]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ? = 1
[1,1,1,0,0,0,1,1,0,0,1,0]
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
=> 0
[1,1,1,0,0,0,1,1,0,1,0,0]
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
=> 0
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3] => [[5,3],[2]]
=> ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ? = 0
[1,1,1,0,0,1,1,0,0,0,1,0]
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
=> 0
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
=> 0
[1,1,1,0,0,1,1,0,1,0,0,0]
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
=> 0
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [3,3] => [[5,3],[2]]
=> ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ? = 0
[1,1,1,0,1,1,0,0,0,0,1,0]
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
=> 0
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
=> 0
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
=> 0
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
=> 0
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [3,3] => [[5,3],[2]]
=> ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ? = 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]]
=> ([(0,3),(1,5),(1,6),(3,6),(4,2),(5,4)],7)
=> ? = 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,2,2] => [[3,2,1,1,1],[1]]
=> ([(0,5),(0,6),(1,3),(1,6),(4,2),(5,4)],7)
=> ? = 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]]
=> ([(0,3),(1,5),(1,6),(3,6),(4,2),(5,4)],7)
=> ? = 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]]
=> ([(0,3),(1,5),(1,6),(3,6),(4,2),(5,4)],7)
=> ? = 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,1,2,2] => [[3,2,1,1,1],[1]]
=> ([(0,5),(0,6),(1,3),(1,6),(4,2),(5,4)],7)
=> ? = 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]]
=> ([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7)
=> ? = 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,1,2,1,2] => [[3,2,2,1,1],[1,1]]
=> ([(0,5),(0,6),(1,3),(1,4),(4,6),(5,2)],7)
=> ? = 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,2,2,1] => [[3,3,2,1,1],[2,1]]
=> ([(0,5),(1,5),(1,6),(2,3),(2,6),(3,4)],7)
=> ? = 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,1,2,2,1] => [[3,3,2,1,1],[2,1]]
=> ([(0,5),(1,5),(1,6),(2,3),(2,6),(3,4)],7)
=> ? = 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,1,2,3] => [[4,2,1,1],[1]]
=> ([(0,5),(0,6),(1,4),(1,6),(4,2),(5,3)],7)
=> ? = 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: St000454
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00173: Integer compositions —rotate front to back⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 50%
Mp00173: Integer compositions —rotate front to back⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 50%
Values
[1,0,1,1,0,0,1,1,0,0]
=> [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[1,0,1,1,0,1,1,0,0,0]
=> [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[1,1,0,0,1,1,0,0,1,0]
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[1,1,0,0,1,1,0,1,0,0]
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[1,1,0,1,1,0,0,0,1,0]
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[1,1,0,1,1,0,0,1,0,0]
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[1,1,0,1,1,0,1,0,0,0]
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 2
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,2,1,1] => [1,2,1,1,1] => ([(0,3),(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 + 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,2,1,1] => [1,2,1,1,1] => ([(0,3),(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 + 2
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,2,1,1] => [1,2,1,1,1] => ([(0,3),(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 + 2
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 2
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,2,1,2] => [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 + 2
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,2,2,1] => [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)
=> ? = 1 + 2
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,2,2,1] => [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)
=> ? = 1 + 2
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 2
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,2,1,2] => [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 + 2
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,2,1,2] => [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 + 2
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,2,2,1] => [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)
=> ? = 1 + 2
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,2,2,1] => [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)
=> ? = 1 + 2
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,2,2,1] => [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)
=> ? = 1 + 2
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 2
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 2
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 2
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,3,2] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 2
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [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
[1,1,0,0,1,0,1,1,0,1,0,0]
=> [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
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [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
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 2
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [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
[1,1,0,0,1,1,0,1,0,1,0,0]
=> [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
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 2
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 1 + 2
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 1 + 2
[1,1,0,0,1,1,1,0,1,0,0,0]
=> [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 1 + 2
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [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
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [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
[1,1,0,1,0,1,1,0,0,0,1,0]
=> [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
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [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
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [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
[1,1,0,1,1,0,0,0,1,0,1,0]
=> [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
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 2
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [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
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [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
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 2
[1,1,0,1,1,0,1,0,0,0,1,0]
=> [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
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [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
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [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
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1 + 2
[1,1,0,1,1,1,0,0,0,0,1,0]
=> [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 1 + 2
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 1 + 2
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 1 + 2
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 1 + 2
[1,1,1,0,0,0,1,1,0,0,1,0]
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 2
[1,1,1,0,0,0,1,1,0,1,0,0]
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 2
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 0 + 2
[1,1,1,0,0,1,1,0,0,0,1,0]
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0 + 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=> [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 0 + 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 0 + 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
=> [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 0 + 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: St000455
Mp00118: Dyck paths —swap returns and last descent⟶ Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000455: Graphs ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 25%
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000455: Graphs ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 25%
Values
[1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0
[1,0,1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> 0
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[1,1,0,0,1,0,1,1,0,1,0,0]
=> [1,1,0,0,1,1,1,0,1,0,0,0]
=> [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,1,1,0,0,0]
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [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
[1,1,0,0,1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0]
=> [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
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,1,0,0]
=> [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[1,1,0,0,1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,1,0,1,0,0]
=> [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
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [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
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0]
=> [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
[1,1,0,1,0,1,1,0,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [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
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0,1,0]
=> [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
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> [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
[1,1,0,1,1,0,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 0
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0,1,1,0,0]
=> [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [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
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> [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
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,1,0,0,0,1,0,1,0]
=> [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)
=> ? = 1
[1,1,0,1,1,0,1,0,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [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
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0,1,0]
=> [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
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,1,0,0,1,1,0,1,0,0,1,0]
=> [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
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,0,0,1,0,1,0]
=> [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)
=> ? = 1
[1,1,0,1,1,1,0,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,0]
=> [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 1
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
=> 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,1,0,1,0,1,1,0,0,0,0,0]
=> [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=> [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
=> [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
=> [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,1,1,0,1,0,0,1,0,0,0,0]
=> [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
=> [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
=> [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0,1,0,1,1,0,0]
=> [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,0,0,1,0,1,0,1,0]
=> [3,1,1,1,1] => ([(0,3),(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)
=> 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
=> [3,1,1,1,1] => ([(0,3),(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)
=> 0
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0,1,1,0,0]
=> [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0,1,0,1,0]
=> [3,1,1,1,1] => ([(0,3),(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)
=> 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
=> [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
=> [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(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.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!