Your data matches 8 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000770
Mapping
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000770: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],3)
 => [1,1,1]
 => [1,1]
 => 1
([],4)
 => [1,1,1,1]
 => [1,1,1]
 => 1
([(2,3)],4)
 => [2,1,1]
 => [1,1]
 => 1
([(0,3),(1,2)],4)
 => [2,2]
 => [2]
 => 2
([],5)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 1
([(3,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => 1
([(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => 1
([(1,4),(2,3)],5)
 => [2,2,1]
 => [2,1]
 => 4
([(0,1),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => 2
([(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => 2
([],6)
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1
([(4,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 1
([(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1
([(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1
([(2,5),(3,4)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 5
([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1
([(1,2),(3,5),(4,5)],6)
 => [3,2,1]
 => [2,1]
 => 4
([(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => [4,2]
 => [2]
 => 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1,1]
 => [1,1]
 => 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => [3,3]
 => [3]
 => 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1
([(0,5),(1,4),(2,3)],6)
 => [2,2,2]
 => [2,2]
 => 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => [4,2]
 => [2]
 => 2
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,2,1]
 => [2,1]
 => 4
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,2]
 => [2]
 => 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,2]
 => [2]
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,3]
 => [3]
 => 3
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,2]
 => [2]
 => 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => 3
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,2]
 => [2]
 => 2
([],7)
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 1
([(5,6)],7)
 => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1
([(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,1,1,1]
 => 1
([(3,6),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => 1
([(2,6),(3,6),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => 1
([(3,6),(4,5)],7)
 => [2,2,1,1,1]
 => [2,1,1,1]
 => 6
([(3,6),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => 1
([(2,3),(4,6),(5,6)],7)
 => [3,2,1,1]
 => [2,1,1]
 => 5
([(4,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,1,1,1]
 => 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [4,2,1]
 => [2,1]
 => 4
([(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [5,2]
 => [2]
 => 2
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1]
 => 1
([(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1,1,1]
 => [1,1,1]
 => 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [3,3,1]
 => [3,1]
 => 5
Description
The major index of an integer partition when read from bottom to top. This is the sum of the positions of the corners of the shape of an integer partition when reading from bottom to top. For example, the partition $\lambda = (8,6,6,4,3,3)$ has corners at positions 3,6,9, and 13, giving a major index of 31.
Matching statistic: St001232
Mapping
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 39% ●values known / values provided: 39%●distinct values known / distinct values provided: 43%
Values
([],3)
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => ? = 1
([],4)
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1
([(2,3)],4)
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 1
([(0,3),(1,2)],4)
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => 2
([],5)
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1
([(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 1
([(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1
([(1,4),(2,3)],5)
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 4
([(0,1),(2,4),(3,4)],5)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2
([(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2
([],6)
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1
([(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 1
([(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 1
([(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => ? = 1
([(2,5),(3,4)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 5
([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => ? = 1
([(1,2),(3,5),(4,5)],6)
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => ? = 4
([(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => ? = 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => ? = 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => ? = 1
([(0,5),(1,4),(2,3)],6)
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => ? = 4
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => ? = 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
([],7)
 => [1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1
([(5,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1
([(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => ? = 1
([(3,6),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => ? = 1
([(2,6),(3,6),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? = 1
([(3,6),(4,5)],7)
 => [2,2,1,1,1]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 6
([(3,6),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => ? = 1
([(2,3),(4,6),(5,6)],7)
 => [3,2,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0,1,0]
 => ? = 5
([(4,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => ? = 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => [5,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? = 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => [4,2,1]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => ? = 4
([(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => ? = 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? = 1
([(3,5),(3,6),(4,5),(4,6)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => ? = 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? = 5
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => ? = 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? = 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? = 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? = 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? = 1
([(1,6),(2,5),(3,4)],7)
 => [2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => ? = 4
([(2,6),(3,5),(4,5),(4,6)],7)
 => [5,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? = 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => [4,2,1]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => ? = 4
([(0,3),(1,2),(4,6),(5,6)],7)
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => ? = 2
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,2,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0,1,0,1,0]
 => ? = 5
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? = 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,2,1]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => ? = 4
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
([(0,1),(0,2),(1,2),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => [5,3]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
([(0,1),(2,3),(2,7),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => [6,2]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => 2
([(0,1),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => [6,2]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => 2
([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => [6,2]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => 2
([(0,1),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => [6,2]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => 2
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001613
(load all 3 compositions to match this statistic)
Mapping
Mp00243: Graphs —weak duplicate order⟶ Posets
Mp00195: Posets —order ideals⟶ Lattices
St001613: Lattices ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 14%
Values
([],3)
 => ([],1)
 => ([(0,1)],2)
 => 1
([],4)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(0,3),(1,2)],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2
([],5)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(1,4),(2,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 4
([(0,1),(2,4),(3,4)],5)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ?
 => ? = 2
([],6)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(2,5),(3,4)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 5
([(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ? = 1
([(1,2),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 4
([(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ? = 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 1
([(0,5),(1,4),(2,3)],6)
 => ([],6)
 => ?
 => ? = 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ?
 => ? = 2
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ?
 => ? = 4
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ?
 => ? = 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([],5)
 => ?
 => ? = 3
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],5)
 => ?
 => ? = 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([],6)
 => ?
 => ? = 3
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ?
 => ? = 2
([],7)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(4,6),(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(3,6),(4,6),(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(3,6),(4,5)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 6
([(3,6),(4,5),(5,6)],7)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ? = 1
([(2,3),(4,6),(5,6)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 5
([(4,5),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ? = 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 4
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ? = 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ? = 1
([(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 5
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 3
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(2,9),(3,8),(4,10),(4,11),(5,7),(5,10),(6,7),(6,11),(7,13),(8,12),(9,12),(10,3),(10,13),(11,2),(11,13),(12,1),(13,8),(13,9)],14)
 => ? = 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ? = 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 1
([(1,6),(2,5),(3,4)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 4
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ?
 => ? = 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ?
 => ? = 4
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],6)
 => ?
 => ? = 2
([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ?
 => ? = 5
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,5),(3,4)],6)
 => ?
 => ? = 2
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ?
 => ? = 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ?
 => ? = 4
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ?
 => ? = 2
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ?
 => ? = 1
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ?
 => ? = 1
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(2,9),(2,11),(3,8),(3,10),(4,12),(4,13),(5,3),(5,12),(5,14),(6,2),(6,13),(6,14),(7,18),(8,16),(9,17),(10,7),(10,16),(11,7),(11,17),(12,8),(12,15),(13,9),(13,15),(14,10),(14,11),(14,15),(15,16),(15,17),(16,18),(17,18),(18,1)],19)
 => ? = 1
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(2,11),(3,7),(3,8),(4,10),(4,13),(5,10),(5,12),(6,3),(6,12),(6,13),(7,15),(8,15),(9,1),(10,2),(10,14),(11,9),(12,7),(12,14),(13,8),(13,14),(14,11),(14,15),(15,9)],16)
 => ? = 1
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(2,9),(2,11),(3,8),(3,10),(4,12),(4,13),(5,3),(5,12),(5,14),(6,2),(6,13),(6,14),(7,18),(8,16),(9,17),(10,7),(10,16),(11,7),(11,17),(12,8),(12,15),(13,9),(13,15),(14,10),(14,11),(14,15),(15,16),(15,17),(16,18),(17,18),(18,1)],19)
 => ? = 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 4
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([(2,5),(3,4)],6)
 => ?
 => ? = 3
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ?
 => ? = 5
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 1
Description
The binary logarithm of the size of the center of a lattice. An element of a lattice is central if it is neutral and has a complement. The subposet induced by central elements is a Boolean lattice.
Matching statistic: St001719
(load all 3 compositions to match this statistic)
Mapping
Mp00243: Graphs —weak duplicate order⟶ Posets
Mp00195: Posets —order ideals⟶ Lattices
St001719: Lattices ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 14%
Values
([],3)
 => ([],1)
 => ([(0,1)],2)
 => 1
([],4)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(0,3),(1,2)],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2
([],5)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(1,4),(2,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 4
([(0,1),(2,4),(3,4)],5)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ?
 => ? = 2
([],6)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(2,5),(3,4)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 5
([(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ? = 1
([(1,2),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 4
([(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ? = 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 1
([(0,5),(1,4),(2,3)],6)
 => ([],6)
 => ?
 => ? = 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ?
 => ? = 2
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ?
 => ? = 4
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ?
 => ? = 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([],5)
 => ?
 => ? = 3
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],5)
 => ?
 => ? = 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([],6)
 => ?
 => ? = 3
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ?
 => ? = 2
([],7)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(4,6),(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(3,6),(4,6),(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(3,6),(4,5)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 6
([(3,6),(4,5),(5,6)],7)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ? = 1
([(2,3),(4,6),(5,6)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 5
([(4,5),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ? = 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 4
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ? = 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ? = 1
([(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 5
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 3
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(2,9),(3,8),(4,10),(4,11),(5,7),(5,10),(6,7),(6,11),(7,13),(8,12),(9,12),(10,3),(10,13),(11,2),(11,13),(12,1),(13,8),(13,9)],14)
 => ? = 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ? = 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 1
([(1,6),(2,5),(3,4)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 4
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ?
 => ? = 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ?
 => ? = 4
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],6)
 => ?
 => ? = 2
([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ?
 => ? = 5
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,5),(3,4)],6)
 => ?
 => ? = 2
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ?
 => ? = 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ?
 => ? = 4
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ?
 => ? = 2
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ?
 => ? = 1
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ?
 => ? = 1
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(2,9),(2,11),(3,8),(3,10),(4,12),(4,13),(5,3),(5,12),(5,14),(6,2),(6,13),(6,14),(7,18),(8,16),(9,17),(10,7),(10,16),(11,7),(11,17),(12,8),(12,15),(13,9),(13,15),(14,10),(14,11),(14,15),(15,16),(15,17),(16,18),(17,18),(18,1)],19)
 => ? = 1
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(2,11),(3,7),(3,8),(4,10),(4,13),(5,10),(5,12),(6,3),(6,12),(6,13),(7,15),(8,15),(9,1),(10,2),(10,14),(11,9),(12,7),(12,14),(13,8),(13,14),(14,11),(14,15),(15,9)],16)
 => ? = 1
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(2,9),(2,11),(3,8),(3,10),(4,12),(4,13),(5,3),(5,12),(5,14),(6,2),(6,13),(6,14),(7,18),(8,16),(9,17),(10,7),(10,16),(11,7),(11,17),(12,8),(12,15),(13,9),(13,15),(14,10),(14,11),(14,15),(15,16),(15,17),(16,18),(17,18),(18,1)],19)
 => ? = 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 4
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([(2,5),(3,4)],6)
 => ?
 => ? = 3
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ?
 => ? = 5
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 1
Description
The number of shortest chains of small intervals from the bottom to the top in a lattice. An interval $[a, b]$ in a lattice is small if $b$ is a join of elements covering $a$.
Matching statistic: St001881
(load all 3 compositions to match this statistic)
Mapping
Mp00243: Graphs —weak duplicate order⟶ Posets
Mp00195: Posets —order ideals⟶ Lattices
St001881: Lattices ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 14%
Values
([],3)
 => ([],1)
 => ([(0,1)],2)
 => 1
([],4)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(0,3),(1,2)],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2
([],5)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(1,4),(2,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 4
([(0,1),(2,4),(3,4)],5)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ?
 => ? = 2
([],6)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(2,5),(3,4)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 5
([(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ? = 1
([(1,2),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 4
([(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ? = 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 1
([(0,5),(1,4),(2,3)],6)
 => ([],6)
 => ?
 => ? = 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ?
 => ? = 2
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ?
 => ? = 4
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ?
 => ? = 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([],5)
 => ?
 => ? = 3
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],5)
 => ?
 => ? = 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([],6)
 => ?
 => ? = 3
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ?
 => ? = 2
([],7)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(4,6),(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(3,6),(4,6),(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(3,6),(4,5)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 6
([(3,6),(4,5),(5,6)],7)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ? = 1
([(2,3),(4,6),(5,6)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 5
([(4,5),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ? = 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 4
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ? = 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ? = 1
([(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 5
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 3
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(2,9),(3,8),(4,10),(4,11),(5,7),(5,10),(6,7),(6,11),(7,13),(8,12),(9,12),(10,3),(10,13),(11,2),(11,13),(12,1),(13,8),(13,9)],14)
 => ? = 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ? = 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 1
([(1,6),(2,5),(3,4)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 4
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ?
 => ? = 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ?
 => ? = 4
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],6)
 => ?
 => ? = 2
([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ?
 => ? = 5
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,5),(3,4)],6)
 => ?
 => ? = 2
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ?
 => ? = 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ?
 => ? = 4
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ?
 => ? = 2
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ?
 => ? = 1
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ?
 => ? = 1
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(2,9),(2,11),(3,8),(3,10),(4,12),(4,13),(5,3),(5,12),(5,14),(6,2),(6,13),(6,14),(7,18),(8,16),(9,17),(10,7),(10,16),(11,7),(11,17),(12,8),(12,15),(13,9),(13,15),(14,10),(14,11),(14,15),(15,16),(15,17),(16,18),(17,18),(18,1)],19)
 => ? = 1
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(2,11),(3,7),(3,8),(4,10),(4,13),(5,10),(5,12),(6,3),(6,12),(6,13),(7,15),(8,15),(9,1),(10,2),(10,14),(11,9),(12,7),(12,14),(13,8),(13,14),(14,11),(14,15),(15,9)],16)
 => ? = 1
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(2,9),(2,11),(3,8),(3,10),(4,12),(4,13),(5,3),(5,12),(5,14),(6,2),(6,13),(6,14),(7,18),(8,16),(9,17),(10,7),(10,16),(11,7),(11,17),(12,8),(12,15),(13,9),(13,15),(14,10),(14,11),(14,15),(15,16),(15,17),(16,18),(17,18),(18,1)],19)
 => ? = 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 4
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([(2,5),(3,4)],6)
 => ?
 => ? = 3
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ?
 => ? = 5
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 1
Description
The number of factors of a lattice as a Cartesian product of lattices. Since the cardinality of a lattice is the product of the cardinalities of its factors, this statistic is one whenever the cardinality of the lattice is prime.
Matching statistic: St001845
(load all 3 compositions to match this statistic)
Mapping
Mp00243: Graphs —weak duplicate order⟶ Posets
Mp00195: Posets —order ideals⟶ Lattices
St001845: Lattices ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 14%
Values
([],3)
 => ([],1)
 => ([(0,1)],2)
 => 0 = 1 - 1
([],4)
 => ([],1)
 => ([(0,1)],2)
 => 0 = 1 - 1
([(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 0 = 1 - 1
([(0,3),(1,2)],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2 - 1
([],5)
 => ([],1)
 => ([(0,1)],2)
 => 0 = 1 - 1
([(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 0 = 1 - 1
([(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 0 = 1 - 1
([(1,4),(2,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 4 - 1
([(0,1),(2,4),(3,4)],5)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2 - 1
([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 0 = 1 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ?
 => ? = 2 - 1
([],6)
 => ([],1)
 => ([(0,1)],2)
 => 0 = 1 - 1
([(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 0 = 1 - 1
([(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 0 = 1 - 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 0 = 1 - 1
([(2,5),(3,4)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 5 - 1
([(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ? = 1 - 1
([(1,2),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 4 - 1
([(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 0 = 1 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ? = 1 - 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 3 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 0 = 1 - 1
([(0,5),(1,4),(2,3)],6)
 => ([],6)
 => ?
 => ? = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ?
 => ? = 2 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ?
 => ? = 4 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ?
 => ? = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([],5)
 => ?
 => ? = 3 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],5)
 => ?
 => ? = 2 - 1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([],6)
 => ?
 => ? = 3 - 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ?
 => ? = 2 - 1
([],7)
 => ([],1)
 => ([(0,1)],2)
 => 0 = 1 - 1
([(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 0 = 1 - 1
([(4,6),(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 0 = 1 - 1
([(3,6),(4,6),(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 0 = 1 - 1
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 0 = 1 - 1
([(3,6),(4,5)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 6 - 1
([(3,6),(4,5),(5,6)],7)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ? = 1 - 1
([(2,3),(4,6),(5,6)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 5 - 1
([(4,5),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 0 = 1 - 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ? = 1 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 4 - 1
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ? = 1 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2 - 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ? = 1 - 1
([(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 5 - 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ? = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 3 - 1
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(2,9),(3,8),(4,10),(4,11),(5,7),(5,10),(6,7),(6,11),(7,13),(8,12),(9,12),(10,3),(10,13),(11,2),(11,13),(12,1),(13,8),(13,9)],14)
 => ? = 1 - 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ? = 1 - 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 0 = 1 - 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 0 = 1 - 1
([(1,6),(2,5),(3,4)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 4 - 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ?
 => ? = 1 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ?
 => ? = 4 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],6)
 => ?
 => ? = 2 - 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ?
 => ? = 5 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,5),(3,4)],6)
 => ?
 => ? = 2 - 1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ?
 => ? = 1 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ?
 => ? = 4 - 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ?
 => ? = 2 - 1
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ?
 => ? = 1 - 1
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ?
 => ? = 1 - 1
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(2,9),(2,11),(3,8),(3,10),(4,12),(4,13),(5,3),(5,12),(5,14),(6,2),(6,13),(6,14),(7,18),(8,16),(9,17),(10,7),(10,16),(11,7),(11,17),(12,8),(12,15),(13,9),(13,15),(14,10),(14,11),(14,15),(15,16),(15,17),(16,18),(17,18),(18,1)],19)
 => ? = 1 - 1
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(2,11),(3,7),(3,8),(4,10),(4,13),(5,10),(5,12),(6,3),(6,12),(6,13),(7,15),(8,15),(9,1),(10,2),(10,14),(11,9),(12,7),(12,14),(13,8),(13,14),(14,11),(14,15),(15,9)],16)
 => ? = 1 - 1
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(2,9),(2,11),(3,8),(3,10),(4,12),(4,13),(5,3),(5,12),(5,14),(6,2),(6,13),(6,14),(7,18),(8,16),(9,17),(10,7),(10,16),(11,7),(11,17),(12,8),(12,15),(13,9),(13,15),(14,10),(14,11),(14,15),(15,16),(15,17),(16,18),(17,18),(18,1)],19)
 => ? = 1 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ? = 4 - 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([(2,5),(3,4)],6)
 => ?
 => ? = 3 - 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ?
 => ? = 5 - 1
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => 0 = 1 - 1
Description
The number of join irreducibles minus the rank of a lattice. A lattice is join-extremal, if this statistic is $0$.
Matching statistic: St001681
Mapping
Mp00243: Graphs —weak duplicate order⟶ Posets
Mp00125: Posets —dual poset⟶ Posets
Mp00195: Posets —order ideals⟶ Lattices
St001681: Lattices ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 14%
Values
([],3)
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 1
([],4)
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(0,3),(1,2)],4)
 => ([],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2
([],5)
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(1,4),(2,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? = 4
([(0,1),(2,4),(3,4)],5)
 => ([],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3)],4)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],5)
 => ?
 => ? = 2
([],6)
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(2,5),(3,4)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? = 5
([(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 1
([(1,2),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? = 4
([(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3)],4)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11)
 => ? = 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3)],4)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => 1
([(0,5),(1,4),(2,3)],6)
 => ([],6)
 => ([],6)
 => ?
 => ? = 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ([(2,5),(3,4)],6)
 => ?
 => ? = 2
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ?
 => ? = 4
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(3,4),(3,5)],6)
 => ?
 => ? = 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([],5)
 => ([],5)
 => ?
 => ? = 3
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],5)
 => ([],5)
 => ?
 => ? = 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? = 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([],6)
 => ([],6)
 => ?
 => ? = 3
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],6)
 => ?
 => ? = 2
([],7)
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 1
([(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(4,6),(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(3,6),(4,6),(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(3,6),(4,5)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? = 6
([(3,6),(4,5),(5,6)],7)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 1
([(2,3),(4,6),(5,6)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? = 5
([(4,5),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3)],4)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? = 4
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11)
 => ? = 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11)
 => ? = 1
([(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? = 5
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 3
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3)],4)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
 => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14)
 => ? = 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11)
 => ? = 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3)],4)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => 1
([(1,6),(2,5),(3,4)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)
 => ?
 => ? = 4
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => ?
 => ? = 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7)
 => ?
 => ? = 4
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],6)
 => ([],6)
 => ?
 => ? = 2
([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ?
 => ? = 5
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,5),(3,4)],6)
 => ([(2,5),(3,4)],6)
 => ?
 => ? = 2
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => ?
 => ? = 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)
 => ?
 => ? = 4
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(3,4),(3,5)],6)
 => ?
 => ? = 2
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ?
 => ? = 1
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ?
 => ? = 1
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
 => ([(0,1),(1,2),(1,3),(1,4),(2,12),(2,13),(3,6),(3,13),(3,14),(4,5),(4,12),(4,14),(5,8),(5,10),(6,9),(6,11),(7,18),(8,16),(9,17),(10,7),(10,16),(11,7),(11,17),(12,8),(12,15),(13,9),(13,15),(14,10),(14,11),(14,15),(15,16),(15,17),(16,18),(17,18)],19)
 => ? = 1
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
 => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,5),(3,6),(3,13),(4,12),(5,9),(5,11),(6,9),(6,10),(7,15),(8,15),(9,14),(10,7),(10,14),(11,8),(11,14),(12,7),(12,8),(13,10),(13,11),(13,12),(14,15)],16)
 => ? = 1
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
 => ([(0,1),(1,2),(1,3),(1,4),(2,12),(2,13),(3,6),(3,13),(3,14),(4,5),(4,12),(4,14),(5,8),(5,10),(6,9),(6,11),(7,18),(8,16),(9,17),(10,7),(10,16),(11,7),(11,17),(12,8),(12,15),(13,9),(13,15),(14,10),(14,11),(14,15),(15,16),(15,17),(16,18),(17,18)],19)
 => ? = 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? = 4
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([(2,5),(3,4)],6)
 => ([(2,5),(3,4)],6)
 => ?
 => ? = 3
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ?
 => ? = 5
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3)],4)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => 1
Description
The number of inclusion-wise minimal subsets of a lattice, whose meet is the bottom element. For example, the pentagon lattice has three such sets: the bottom element, and the two antichains of size two. The cube is the smallest lattice which has such sets of three different sizes: the bottom element, six antichains of size two and one antichain of size three.
Matching statistic: St001677
Mapping
Mp00243: Graphs —weak duplicate order⟶ Posets
Mp00125: Posets —dual poset⟶ Posets
Mp00195: Posets —order ideals⟶ Lattices
St001677: Lattices ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 14%
Values
([],3)
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 0 = 1 - 1
([],4)
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 0 = 1 - 1
([(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 0 = 1 - 1
([(0,3),(1,2)],4)
 => ([],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2 - 1
([],5)
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 0 = 1 - 1
([(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 0 = 1 - 1
([(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 0 = 1 - 1
([(1,4),(2,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? = 4 - 1
([(0,1),(2,4),(3,4)],5)
 => ([],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2 - 1
([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3)],4)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => 0 = 1 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],5)
 => ?
 => ? = 2 - 1
([],6)
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 0 = 1 - 1
([(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 0 = 1 - 1
([(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 0 = 1 - 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 0 = 1 - 1
([(2,5),(3,4)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? = 5 - 1
([(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 1 - 1
([(1,2),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? = 4 - 1
([(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3)],4)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => 0 = 1 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11)
 => ? = 1 - 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 0 = 1 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 3 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3)],4)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => 0 = 1 - 1
([(0,5),(1,4),(2,3)],6)
 => ([],6)
 => ([],6)
 => ?
 => ? = 2 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(2,5),(3,4)],6)
 => ([(2,5),(3,4)],6)
 => ?
 => ? = 2 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ?
 => ? = 4 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(3,4),(3,5)],6)
 => ?
 => ? = 2 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([],5)
 => ([],5)
 => ?
 => ? = 3 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],5)
 => ([],5)
 => ?
 => ? = 2 - 1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? = 1 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([],6)
 => ([],6)
 => ?
 => ? = 3 - 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],6)
 => ([],6)
 => ?
 => ? = 2 - 1
([],7)
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 0 = 1 - 1
([(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 0 = 1 - 1
([(4,6),(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 0 = 1 - 1
([(3,6),(4,6),(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 0 = 1 - 1
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 0 = 1 - 1
([(3,6),(4,5)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? = 6 - 1
([(3,6),(4,5),(5,6)],7)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 1 - 1
([(2,3),(4,6),(5,6)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? = 5 - 1
([(4,5),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3)],4)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => 0 = 1 - 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 1 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? = 4 - 1
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11)
 => ? = 1 - 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 2 - 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11)
 => ? = 1 - 1
([(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 0 = 1 - 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? = 5 - 1
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 1 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
 => ? = 3 - 1
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3)],4)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => 0 = 1 - 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
 => ([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14)
 => ? = 1 - 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11)
 => ? = 1 - 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 0 = 1 - 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3)],4)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => 0 = 1 - 1
([(1,6),(2,5),(3,4)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)
 => ?
 => ? = 4 - 1
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => ?
 => ? = 1 - 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7)
 => ?
 => ? = 4 - 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],6)
 => ([],6)
 => ?
 => ? = 2 - 1
([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ?
 => ? = 5 - 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,5),(3,4)],6)
 => ([(2,5),(3,4)],6)
 => ?
 => ? = 2 - 1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => ?
 => ? = 1 - 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)
 => ?
 => ? = 4 - 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(3,4),(3,5)],6)
 => ?
 => ? = 2 - 1
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ?
 => ? = 1 - 1
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ?
 => ? = 1 - 1
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
 => ([(0,1),(1,2),(1,3),(1,4),(2,12),(2,13),(3,6),(3,13),(3,14),(4,5),(4,12),(4,14),(5,8),(5,10),(6,9),(6,11),(7,18),(8,16),(9,17),(10,7),(10,16),(11,7),(11,17),(12,8),(12,15),(13,9),(13,15),(14,10),(14,11),(14,15),(15,16),(15,17),(16,18),(17,18)],19)
 => ? = 1 - 1
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
 => ([(0,1),(1,2),(1,3),(2,4),(2,13),(3,5),(3,6),(3,13),(4,12),(5,9),(5,11),(6,9),(6,10),(7,15),(8,15),(9,14),(10,7),(10,14),(11,8),(11,14),(12,7),(12,8),(13,10),(13,11),(13,12),(14,15)],16)
 => ? = 1 - 1
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
 => ([(0,1),(1,2),(1,3),(1,4),(2,12),(2,13),(3,6),(3,13),(3,14),(4,5),(4,12),(4,14),(5,8),(5,10),(6,9),(6,11),(7,18),(8,16),(9,17),(10,7),(10,16),(11,7),(11,17),(12,8),(12,15),(13,9),(13,15),(14,10),(14,11),(14,15),(15,16),(15,17),(16,18),(17,18)],19)
 => ? = 1 - 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? = 4 - 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
 => ([(2,5),(3,4)],6)
 => ([(2,5),(3,4)],6)
 => ?
 => ? = 3 - 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ?
 => ? = 5 - 1
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3)],4)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => 0 = 1 - 1
Description
The number of non-degenerate subsets of a lattice whose meet is the bottom element. A subset whose meet is the bottom element is non-degenerate, if it neither contains the bottom, nor the top element of the lattice.