Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001875
Mapping
Mp00141: Binary trees —pruning number to logarithmic height⟶ Dyck paths
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001875: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[.,[[.,[[.,.],.]],.]]
 => [1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 3
[[.,[[.,[.,.]],.]],.]
 => [1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 3
[.,[.,[[.,[.,[.,.]]],.]]]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1,1],[1,1]]
 => ([(0,2),(2,1)],3)
 => 3
[.,[.,[[.,[[.,.],.]],.]]]
 => [1,0,1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1,1],[1]]
 => ([(0,2),(2,1)],3)
 => 3
[.,[[.,.],[.,[[.,.],.]]]]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [[3,2,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 3
[.,[[.,.],[[.,.],[.,.]]]]
 => [1,0,1,1,1,0,0,1,1,0,0,0]
 => [[3,3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 3
[.,[[.,.],[[.,[.,.]],.]]]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [[3,3,2,1],[2]]
 => ([(0,2),(2,1)],3)
 => 3
[.,[[.,[.,[[.,.],.]]],.]]
 => [1,0,1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2,1],[1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[.,[[.,[[.,.],[.,.]]],.]]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2,1],[1,1]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[.,[[.,[[.,[.,.]],.]],.]]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2,1],[2,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 4
[.,[[.,[[[.,.],.],.]],.]]
 => [1,0,1,1,0,0,1,1,0,1,0,0]
 => [[4,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 3
[.,[[[.,.],[.,[.,.]]],.]]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3,1],[2,1]]
 => ([(0,2),(2,1)],3)
 => 3
[.,[[[.,.],[[.,.],.]],.]]
 => [1,0,1,1,0,1,1,0,0,1,0,0]
 => [[4,3,1],[1]]
 => ([(0,2),(2,1)],3)
 => 3
[.,[[[.,[[.,.],.]],.],.]]
 => [1,0,1,1,0,1,0,0,1,1,0,0]
 => [[4,3,1],[2]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[[.,.],[.,[[.,.],[.,.]]]]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [[3,3,2,2],[1,1]]
 => ([(0,2),(2,1)],3)
 => 3
[[.,.],[.,[[.,[.,.]],.]]]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [[3,3,2,2],[2,1]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[[.,.],[[.,.],[.,[.,.]]]]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => [[3,3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 3
[[.,.],[[.,.],[[.,.],.]]]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => [[4,3,2],[1]]
 => ([(0,2),(2,1)],3)
 => 3
[[.,.],[[.,[[.,.],.]],.]]
 => [1,1,1,0,0,1,0,0,1,1,0,0]
 => [[4,3,2],[2]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[[.,.],[[[.,.],[.,.]],.]]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [[4,4,2],[2]]
 => ([(0,2),(2,1)],3)
 => 3
[[.,[.,[[.,[.,.]],.]]],.]
 => [1,1,0,0,1,0,1,1,0,0,1,0]
 => [[3,3,2,2],[2,1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[[.,[[.,.],[.,[.,.]]]],.]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [[3,3,3,2],[2,1,1]]
 => ([(0,2),(2,1)],3)
 => 3
[[.,[[.,.],[[.,.],.]]],.]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => [[4,3,2],[1,1]]
 => ([(0,2),(2,1)],3)
 => 3
[[.,[[.,[.,[.,.]]],.]],.]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [[3,3,3,2],[2,2,1]]
 => ([(0,2),(2,1)],3)
 => 3
[[.,[[.,[[.,.],.]],.]],.]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 4
[[.,[[[.,.],[.,.]],.]],.]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => [[4,4,2],[2,1]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[[.,[[[.,[.,.]],.],.]],.]
 => [1,1,0,0,1,1,0,1,0,0,1,0]
 => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[[[.,.],[.,[[.,.],.]]],.]
 => [1,1,0,1,1,0,0,0,1,1,0,0]
 => [[4,3,3],[2,1]]
 => ([(0,2),(2,1)],3)
 => 3
[[[.,.],[[.,.],[.,.]]],.]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [[4,4,3],[2,1]]
 => ([(0,2),(2,1)],3)
 => 3
[[[.,.],[[.,[.,.]],.]],.]
 => [1,1,0,1,1,0,0,1,0,0,1,0]
 => [[4,4,3],[3,1]]
 => ([(0,2),(2,1)],3)
 => 3
[[[.,[[.,[.,.]],.]],.],.]
 => [1,1,0,1,0,0,1,1,0,0,1,0]
 => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 3
[[[.,[[[.,.],.],.]],.],.]
 => [1,1,0,1,0,0,1,1,0,1,0,0]
 => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 3
[.,[.,[.,[[.,[.,[.,.]]],.]]]]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1,1,1],[1,1]]
 => ([(0,2),(2,1)],3)
 => 3
[.,[.,[.,[[.,[[.,.],.]],.]]]]
 => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1,1,1],[1]]
 => ([(0,2),(2,1)],3)
 => 3
[.,[.,[[.,[.,[.,[.,.]]]],.]]]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2,1,1],[1,1,1]]
 => ([(0,2),(2,1)],3)
 => 3
[.,[.,[[.,[.,[[.,.],.]]],.]]]
 => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2,1,1],[1,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 4
[.,[.,[[.,[[.,[.,.]],.]],.]]]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2,1,1],[2,1]]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => 5
[.,[.,[[.,[[[.,.],.],.]],.]]]
 => [1,0,1,0,1,1,0,0,1,1,0,1,0,0]
 => [[4,2,1,1],[1]]
 => ([(0,2),(2,1)],3)
 => 3
[.,[.,[[[.,[.,[.,.]]],.],.]]]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3,1,1],[2,2]]
 => ([(0,2),(2,1)],3)
 => 3
[.,[.,[[[.,[[.,.],.]],.],.]]]
 => [1,0,1,0,1,1,0,1,0,0,1,1,0,0]
 => [[4,3,1,1],[2]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[.,[[[.,[[.,.],.]],.],[.,.]]]
 => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
 => [[4,4,3,1],[1]]
 => ([(0,2),(2,1)],3)
 => 3
[.,[[.,[.,[.,[[.,.],.]]]],.]]
 => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [[3,2,2,2,1],[1,1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[.,[[.,[.,[[.,[.,.]],.]]],.]]
 => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [[3,3,2,2,1],[2,1,1]]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => 5
[.,[[.,[.,[[[.,.],.],.]]],.]]
 => [1,0,1,1,0,0,1,0,1,1,0,1,0,0]
 => [[4,2,2,1],[1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[.,[[.,[[.,[.,[.,.]]],.]],.]]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [[3,3,3,2,1],[2,2,1]]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => 5
[.,[[.,[[.,[[.,.],.]],.]],.]]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [[4,3,2,1],[2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => 6
[.,[[.,[[[.,[.,.]],.],.]],.]]
 => [1,0,1,1,0,0,1,1,0,1,0,0,1,0]
 => [[4,4,2,1],[3,1]]
 => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => 5
[.,[[.,[[[[.,.],.],.],.]],.]]
 => [1,0,1,1,0,0,1,1,0,1,0,1,0,0]
 => [[5,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 3
[.,[[[.,[.,[[.,.],.]]],.],.]]
 => [1,0,1,1,0,1,0,0,1,0,1,1,0,0]
 => [[4,3,3,1],[2,2]]
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 4
[.,[[[.,[[.,[.,.]],.]],.],.]]
 => [1,0,1,1,0,1,0,0,1,1,0,0,1,0]
 => [[4,4,3,1],[3,2]]
 => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => 5
Description
The number of simple modules with projective dimension at most 1.
Matching statistic: St001622
Mapping
Mp00141: Binary trees —pruning number to logarithmic height⟶ Dyck paths
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001622: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[.,[[.,[[.,.],.]],.]]
 => [1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[[.,[[.,[.,.]],.]],.]
 => [1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[.,[.,[[.,[.,[.,.]]],.]]]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1,1],[1,1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[.,[.,[[.,[[.,.],.]],.]]]
 => [1,0,1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1,1],[1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[.,[[.,.],[.,[[.,.],.]]]]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [[3,2,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[.,[[.,.],[[.,.],[.,.]]]]
 => [1,0,1,1,1,0,0,1,1,0,0,0]
 => [[3,3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[.,[[.,.],[[.,[.,.]],.]]]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [[3,3,2,1],[2]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[.,[[.,[.,[[.,.],.]]],.]]
 => [1,0,1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2,1],[1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
[.,[[.,[[.,.],[.,.]]],.]]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2,1],[1,1]]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 4 - 1
[.,[[.,[[.,[.,.]],.]],.]]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2,1],[2,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 3 = 4 - 1
[.,[[.,[[[.,.],.],.]],.]]
 => [1,0,1,1,0,0,1,1,0,1,0,0]
 => [[4,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[.,[[[.,.],[.,[.,.]]],.]]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3,1],[2,1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[.,[[[.,.],[[.,.],.]],.]]
 => [1,0,1,1,0,1,1,0,0,1,0,0]
 => [[4,3,1],[1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[.,[[[.,[[.,.],.]],.],.]]
 => [1,0,1,1,0,1,0,0,1,1,0,0]
 => [[4,3,1],[2]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
[[.,.],[.,[[.,.],[.,.]]]]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [[3,3,2,2],[1,1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[[.,.],[.,[[.,[.,.]],.]]]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [[3,3,2,2],[2,1]]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 4 - 1
[[.,.],[[.,.],[.,[.,.]]]]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => [[3,3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[[.,.],[[.,.],[[.,.],.]]]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => [[4,3,2],[1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[[.,.],[[.,[[.,.],.]],.]]
 => [1,1,1,0,0,1,0,0,1,1,0,0]
 => [[4,3,2],[2]]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 4 - 1
[[.,.],[[[.,.],[.,.]],.]]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [[4,4,2],[2]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[[.,[.,[[.,[.,.]],.]]],.]
 => [1,1,0,0,1,0,1,1,0,0,1,0]
 => [[3,3,2,2],[2,1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
[[.,[[.,.],[.,[.,.]]]],.]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [[3,3,3,2],[2,1,1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[[.,[[.,.],[[.,.],.]]],.]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => [[4,3,2],[1,1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[[.,[[.,[.,[.,.]]],.]],.]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [[3,3,3,2],[2,2,1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[[.,[[.,[[.,.],.]],.]],.]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 3 = 4 - 1
[[.,[[[.,.],[.,.]],.]],.]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => [[4,4,2],[2,1]]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 4 - 1
[[.,[[[.,[.,.]],.],.]],.]
 => [1,1,0,0,1,1,0,1,0,0,1,0]
 => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
[[[.,.],[.,[[.,.],.]]],.]
 => [1,1,0,1,1,0,0,0,1,1,0,0]
 => [[4,3,3],[2,1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[[[.,.],[[.,.],[.,.]]],.]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [[4,4,3],[2,1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[[[.,.],[[.,[.,.]],.]],.]
 => [1,1,0,1,1,0,0,1,0,0,1,0]
 => [[4,4,3],[3,1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[[[.,[[.,[.,.]],.]],.],.]
 => [1,1,0,1,0,0,1,1,0,0,1,0]
 => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[[[.,[[[.,.],.],.]],.],.]
 => [1,1,0,1,0,0,1,1,0,1,0,0]
 => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[.,[.,[.,[[.,[.,[.,.]]],.]]]]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1,1,1],[1,1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[.,[.,[.,[[.,[[.,.],.]],.]]]]
 => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1,1,1],[1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[.,[.,[[.,[.,[.,[.,.]]]],.]]]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2,1,1],[1,1,1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[.,[.,[[.,[.,[[.,.],.]]],.]]]
 => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2,1,1],[1,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 3 = 4 - 1
[.,[.,[[.,[[.,[.,.]],.]],.]]]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2,1,1],[2,1]]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => 4 = 5 - 1
[.,[.,[[.,[[[.,.],.],.]],.]]]
 => [1,0,1,0,1,1,0,0,1,1,0,1,0,0]
 => [[4,2,1,1],[1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[.,[.,[[[.,[.,[.,.]]],.],.]]]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3,1,1],[2,2]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[.,[.,[[[.,[[.,.],.]],.],.]]]
 => [1,0,1,0,1,1,0,1,0,0,1,1,0,0]
 => [[4,3,1,1],[2]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
[.,[[[.,[[.,.],.]],.],[.,.]]]
 => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
 => [[4,4,3,1],[1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[.,[[.,[.,[.,[[.,.],.]]]],.]]
 => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [[3,2,2,2,1],[1,1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
[.,[[.,[.,[[.,[.,.]],.]]],.]]
 => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [[3,3,2,2,1],[2,1,1]]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => 4 = 5 - 1
[.,[[.,[.,[[[.,.],.],.]]],.]]
 => [1,0,1,1,0,0,1,0,1,1,0,1,0,0]
 => [[4,2,2,1],[1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
[.,[[.,[[.,[.,[.,.]]],.]],.]]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [[3,3,3,2,1],[2,2,1]]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => 4 = 5 - 1
[.,[[.,[[.,[[.,.],.]],.]],.]]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [[4,3,2,1],[2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => 5 = 6 - 1
[.,[[.,[[[.,[.,.]],.],.]],.]]
 => [1,0,1,1,0,0,1,1,0,1,0,0,1,0]
 => [[4,4,2,1],[3,1]]
 => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => 4 = 5 - 1
[.,[[.,[[[[.,.],.],.],.]],.]]
 => [1,0,1,1,0,0,1,1,0,1,0,1,0,0]
 => [[5,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => 2 = 3 - 1
[.,[[[.,[.,[[.,.],.]]],.],.]]
 => [1,0,1,1,0,1,0,0,1,0,1,1,0,0]
 => [[4,3,3,1],[2,2]]
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 3 = 4 - 1
[.,[[[.,[[.,[.,.]],.]],.],.]]
 => [1,0,1,1,0,1,0,0,1,1,0,0,1,0]
 => [[4,4,3,1],[3,2]]
 => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => 4 = 5 - 1
Description
The number of join-irreducible elements of a lattice. An element $j$ of a lattice $L$ is '''join irreducible''' if it is not the least element and if $j=x\vee y$, then $j\in\{x,y\}$ for all $x,y\in L$.