Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001879
(load all 16 compositions to match this statistic)
Mapping
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00223: Permutations —runsort⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0,1,0]
 => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
 => 2
[1,1,0,1,0,0]
 => [2,3,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 2
[1,1,1,0,0,0]
 => [3,2,1] => [1,2,3] => ([(0,2),(2,1)],3)
 => 2
[1,0,1,0,1,0,1,0]
 => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 3
[1,0,1,1,0,0,1,0]
 => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[1,1,0,1,0,1,0,0]
 => [2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 3
[1,1,1,0,1,0,0,0]
 => [4,2,3,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 3
[1,1,1,1,0,0,0,0]
 => [4,3,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 3
[1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[1,0,1,0,1,1,0,0,1,0]
 => [1,2,4,3,5] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 5
[1,0,1,1,0,0,1,0,1,0]
 => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 5
[1,0,1,1,0,1,0,0,1,0]
 => [1,3,4,2,5] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 6
[1,0,1,1,1,0,0,1,0,0]
 => [1,4,3,5,2] => [1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 6
[1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => [1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 6
[1,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[1,1,0,1,1,0,0,1,0,0]
 => [2,4,3,5,1] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 5
[1,1,1,0,1,0,1,0,0,0]
 => [5,2,3,4,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[1,1,1,0,1,1,0,0,0,0]
 => [5,2,4,3,1] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 5
[1,1,1,1,0,0,1,0,0,0]
 => [5,3,2,4,1] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 5
[1,1,1,1,0,1,0,0,0,0]
 => [5,3,4,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[1,1,1,1,1,0,0,0,0,0]
 => [5,4,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,2,3,5,4,6] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => 6
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,2,4,3,5,6] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => 6
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,2,4,5,3,6] => [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => 7
[1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,2,5,4,6,3] => [1,2,5,3,4,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => 7
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,3,2,4,5,6] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => 6
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,3,4,2,5,6] => [1,3,4,2,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => 7
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,3,4,5,2,6] => [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => 8
[1,0,1,1,0,1,1,0,0,1,0,0]
 => [1,3,5,4,6,2] => [1,3,5,2,4,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 7
[1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,4,3,5,6,2] => [1,4,2,3,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => 7
[1,0,1,1,1,0,1,0,0,1,0,0]
 => [1,5,3,4,6,2] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => 8
[1,1,0,0,1,0,1,1,0,0,1,0]
 => [2,1,3,5,4,6] => [1,3,5,2,4,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 7
[1,1,0,0,1,1,0,0,1,0,1,0]
 => [2,1,4,3,5,6] => [1,4,2,3,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => 7
[1,1,0,0,1,1,0,1,0,0,1,0]
 => [2,1,4,5,3,6] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => 8
[1,1,0,0,1,1,1,0,0,1,0,0]
 => [2,1,5,4,6,3] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => 8
[1,1,0,1,0,0,1,1,0,0,1,0]
 => [2,3,1,5,4,6] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => 8
[1,1,0,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,6,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[1,1,0,1,0,1,1,0,0,1,0,0]
 => [2,3,5,4,6,1] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => 6
[1,1,0,1,1,0,0,1,0,1,0,0]
 => [2,4,3,5,6,1] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => 6
[1,1,0,1,1,0,1,0,0,1,0,0]
 => [2,5,3,4,6,1] => [1,2,5,3,4,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => 7
[1,1,1,0,0,0,1,1,0,0,1,0]
 => [3,2,1,5,4,6] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => 8
[1,1,1,0,0,1,1,0,0,1,0,0]
 => [3,2,5,4,6,1] => [1,2,5,3,4,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => 7
[1,1,1,0,1,0,1,0,1,0,0,0]
 => [6,2,3,4,5,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [6,2,3,5,4,1] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => 6
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [6,2,4,3,5,1] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => 6
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [6,2,4,5,3,1] => [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => 7
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [6,2,5,4,3,1] => [1,2,5,3,4,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => 7
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [6,3,2,4,5,1] => [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => 7
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [6,3,2,5,4,1] => [1,2,5,3,4,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => 7
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
Matching statistic: St001880
Mapping
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 45%
Values
[1,0,1,0,1,0]
 => [1,2,3] => [.,[.,[.,.]]]
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
[1,1,0,1,0,0]
 => [2,3,1] => [[.,[.,.]],.]
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
[1,1,1,0,0,0]
 => [3,2,1] => [[[.,.],.],.]
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
[1,0,1,0,1,0,1,0]
 => [1,2,3,4] => [.,[.,[.,[.,.]]]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[1,0,1,1,0,0,1,0]
 => [1,3,2,4] => [.,[[.,.],[.,.]]]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 4 + 1
[1,1,0,1,0,1,0,0]
 => [2,3,4,1] => [[.,[.,[.,.]]],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[1,1,1,0,1,0,0,0]
 => [4,2,3,1] => [[[.,.],[.,.]],.]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 3 + 1
[1,1,1,1,0,0,0,0]
 => [4,3,2,1] => [[[[.,.],.],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[1,0,1,0,1,1,0,0,1,0]
 => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 5 + 1
[1,0,1,1,0,0,1,0,1,0]
 => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 5 + 1
[1,0,1,1,0,1,0,0,1,0]
 => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 6 + 1
[1,0,1,1,1,0,0,1,0,0]
 => [1,4,3,5,2] => [.,[[[.,.],[.,.]],.]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 6 + 1
[1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 6 + 1
[1,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[1,1,0,1,1,0,0,1,0,0]
 => [2,4,3,5,1] => [[.,[[.,.],[.,.]]],.]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 5 + 1
[1,1,1,0,1,0,1,0,0,0]
 => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 4 + 1
[1,1,1,0,1,1,0,0,0,0]
 => [5,2,4,3,1] => [[[.,.],[[.,.],.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 5 + 1
[1,1,1,1,0,0,1,0,0,0]
 => [5,3,2,4,1] => [[[[.,.],.],[.,.]],.]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 5 + 1
[1,1,1,1,0,1,0,0,0,0]
 => [5,3,4,2,1] => [[[[.,.],[.,.]],.],.]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 4 + 1
[1,1,1,1,1,0,0,0,0,0]
 => [5,4,3,2,1] => [[[[[.,.],.],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ? = 6 + 1
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 6 + 1
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 7 + 1
[1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,2,5,4,6,3] => [.,[.,[[[.,.],[.,.]],.]]]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ? = 7 + 1
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]]
 => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ? = 6 + 1
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]]
 => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => ? = 7 + 1
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,3,4,5,2,6] => [.,[[.,[.,[.,.]]],[.,.]]]
 => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ? = 8 + 1
[1,0,1,1,0,1,1,0,0,1,0,0]
 => [1,3,5,4,6,2] => [.,[[.,[[.,.],[.,.]]],.]]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ? = 7 + 1
[1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,4,3,5,6,2] => [.,[[[.,.],[.,[.,.]]],.]]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 7 + 1
[1,0,1,1,1,0,1,0,0,1,0,0]
 => [1,5,3,4,6,2] => [.,[[[.,.],[.,[.,.]]],.]]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 8 + 1
[1,1,0,0,1,0,1,1,0,0,1,0]
 => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => ? = 7 + 1
[1,1,0,0,1,1,0,0,1,0,1,0]
 => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 7 + 1
[1,1,0,0,1,1,0,1,0,0,1,0]
 => [2,1,4,5,3,6] => [[.,.],[[.,[.,.]],[.,.]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 8 + 1
[1,1,0,0,1,1,1,0,0,1,0,0]
 => [2,1,5,4,6,3] => [[.,.],[[[.,.],[.,.]],.]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => ? = 8 + 1
[1,1,0,1,0,0,1,1,0,0,1,0]
 => [2,3,1,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 8 + 1
[1,1,0,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[1,1,0,1,0,1,1,0,0,1,0,0]
 => [2,3,5,4,6,1] => [[.,[.,[[.,.],[.,.]]]],.]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ? = 6 + 1
[1,1,0,1,1,0,0,1,0,1,0,0]
 => [2,4,3,5,6,1] => [[.,[[.,.],[.,[.,.]]]],.]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 6 + 1
[1,1,0,1,1,0,1,0,0,1,0,0]
 => [2,5,3,4,6,1] => [[.,[[.,.],[.,[.,.]]]],.]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 7 + 1
[1,1,1,0,0,0,1,1,0,0,1,0]
 => [3,2,1,5,4,6] => [[[.,.],.],[[.,.],[.,.]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 8 + 1
[1,1,1,0,0,1,1,0,0,1,0,0]
 => [3,2,5,4,6,1] => [[[.,.],[[.,.],[.,.]]],.]
 => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
 => ? = 7 + 1
[1,1,1,0,1,0,1,0,1,0,0,0]
 => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.]
 => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ? = 5 + 1
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [6,2,3,5,4,1] => [[[.,.],[.,[[.,.],.]]],.]
 => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ? = 6 + 1
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [6,2,4,3,5,1] => [[[.,.],[[.,.],[.,.]]],.]
 => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
 => ? = 6 + 1
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [6,2,4,5,3,1] => [[[.,.],[[.,[.,.]],.]],.]
 => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ? = 7 + 1
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [6,2,5,4,3,1] => [[[.,.],[[[.,.],.],.]],.]
 => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ? = 7 + 1
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.]
 => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => ? = 7 + 1
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [6,3,2,5,4,1] => [[[[.,.],.],[[.,.],.]],.]
 => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => ? = 7 + 1
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [6,3,4,2,5,1] => [[[[.,.],[.,.]],[.,.]],.]
 => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
 => ? = 7 + 1
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [6,3,4,5,2,1] => [[[[.,.],[.,[.,.]]],.],.]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 5 + 1
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [6,3,5,4,2,1] => [[[[.,.],[[.,.],.]],.],.]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 6 + 1
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.]
 => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ? = 7 + 1
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [6,4,3,5,2,1] => [[[[[.,.],.],[.,.]],.],.]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 6 + 1
[1,1,1,1,1,0,1,0,0,0,0,0]
 => [6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 5 + 1
[1,1,1,1,1,1,0,0,0,0,0,0]
 => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]]
 => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
 => ? = 7 + 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]]
 => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
 => ? = 7 + 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,[.,.]],[.,.]]]]]
 => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
 => ? = 8 + 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,2,3,6,5,7,4] => [.,[.,[.,[[[.,.],[.,.]],.]]]]
 => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
 => ? = 8 + 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
 => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
 => ? = 7 + 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,6,7,1] => [[.,[.,[.,[.,[.,[.,.]]]]]],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.