Your data matches 4 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000772
Mapping
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000772: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => => [1] => ([],1)
 => 1
[1,2] => 1 => [1,1] => ([(0,1)],2)
 => 1
[1,2,3] => 11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 2
[2,1,3] => 01 => [2,1] => ([(0,2),(1,2)],3)
 => 1
[1,2,3,4] => 111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[1,3,2,4] => 101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[2,1,3,4] => 011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[2,3,1,4] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[3,1,2,4] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[3,2,1,4] => 001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[1,2,3,4,5] => 1111 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
[1,2,4,3,5] => 1101 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,3,2,4,5] => 1011 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,3,4,2,5] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[1,4,2,3,5] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[1,4,3,2,5] => 1001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[2,1,3,4,5] => 0111 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[2,1,4,3,5] => 0101 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[2,3,1,4,5] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[2,3,4,1,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[2,4,1,3,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[2,4,3,1,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[3,1,2,4,5] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[3,1,4,2,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[3,2,1,4,5] => 0011 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
[3,2,4,1,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[3,4,1,2,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[3,4,2,1,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[4,1,2,3,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[4,1,3,2,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[4,2,1,3,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[4,2,3,1,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[4,3,1,2,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[4,3,2,1,5] => 0001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[1,2,3,4,5,6] => 11111 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
[1,2,3,5,4,6] => 11101 => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,2,4,3,5,6] => 11011 => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,2,4,5,3,6] => 11001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
[1,2,5,3,4,6] => 11001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
[1,2,5,4,3,6] => 11001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
[1,3,2,4,5,6] => 10111 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,3,2,5,4,6] => 10101 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,3,4,2,5,6] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
[1,3,4,5,2,6] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,3,5,2,4,6] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,3,5,4,2,6] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,4,2,3,5,6] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
[1,4,2,5,3,6] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,4,3,2,5,6] => 10011 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
[1,4,3,5,2,6] => 10001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
Description
The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. The distance Laplacian of a graph is the (symmetric) matrix with row and column sums $0$, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue. For example, the cycle on four vertices has distance Laplacian $$ \left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right). $$ Its eigenvalues are $0,4,4,6$, so the statistic is $1$. The path on four vertices has eigenvalues $0, 4.7\dots, 6, 9.2\dots$ and therefore also statistic $1$. The graphs with statistic $n-1$, $n-2$ and $n-3$ have been characterised, see [1].
Matching statistic: St000383
Mapping
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00172: Integer compositions —rotate back to front⟶ Integer compositions
St000383: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => => [] => ? => ? = 1
[1,2] => 1 => [1] => [1] => 1
[1,2,3] => 11 => [2] => [2] => 2
[2,1,3] => 01 => [1,1] => [1,1] => 1
[1,2,3,4] => 111 => [3] => [3] => 3
[1,3,2,4] => 101 => [1,1,1] => [1,1,1] => 1
[2,1,3,4] => 011 => [1,2] => [2,1] => 1
[2,3,1,4] => 001 => [2,1] => [1,2] => 2
[3,1,2,4] => 001 => [2,1] => [1,2] => 2
[3,2,1,4] => 001 => [2,1] => [1,2] => 2
[1,2,3,4,5] => 1111 => [4] => [4] => 4
[1,2,4,3,5] => 1101 => [2,1,1] => [1,2,1] => 1
[1,3,2,4,5] => 1011 => [1,1,2] => [2,1,1] => 1
[1,3,4,2,5] => 1001 => [1,2,1] => [1,1,2] => 2
[1,4,2,3,5] => 1001 => [1,2,1] => [1,1,2] => 2
[1,4,3,2,5] => 1001 => [1,2,1] => [1,1,2] => 2
[2,1,3,4,5] => 0111 => [1,3] => [3,1] => 1
[2,1,4,3,5] => 0101 => [1,1,1,1] => [1,1,1,1] => 1
[2,3,1,4,5] => 0011 => [2,2] => [2,2] => 2
[2,3,4,1,5] => 0001 => [3,1] => [1,3] => 3
[2,4,1,3,5] => 0001 => [3,1] => [1,3] => 3
[2,4,3,1,5] => 0001 => [3,1] => [1,3] => 3
[3,1,2,4,5] => 0011 => [2,2] => [2,2] => 2
[3,1,4,2,5] => 0001 => [3,1] => [1,3] => 3
[3,2,1,4,5] => 0011 => [2,2] => [2,2] => 2
[3,2,4,1,5] => 0001 => [3,1] => [1,3] => 3
[3,4,1,2,5] => 0001 => [3,1] => [1,3] => 3
[3,4,2,1,5] => 0001 => [3,1] => [1,3] => 3
[4,1,2,3,5] => 0001 => [3,1] => [1,3] => 3
[4,1,3,2,5] => 0001 => [3,1] => [1,3] => 3
[4,2,1,3,5] => 0001 => [3,1] => [1,3] => 3
[4,2,3,1,5] => 0001 => [3,1] => [1,3] => 3
[4,3,1,2,5] => 0001 => [3,1] => [1,3] => 3
[4,3,2,1,5] => 0001 => [3,1] => [1,3] => 3
[1,2,3,4,5,6] => 11111 => [5] => [5] => 5
[1,2,3,5,4,6] => 11101 => [3,1,1] => [1,3,1] => 1
[1,2,4,3,5,6] => 11011 => [2,1,2] => [2,2,1] => 1
[1,2,4,5,3,6] => 11001 => [2,2,1] => [1,2,2] => 2
[1,2,5,3,4,6] => 11001 => [2,2,1] => [1,2,2] => 2
[1,2,5,4,3,6] => 11001 => [2,2,1] => [1,2,2] => 2
[1,3,2,4,5,6] => 10111 => [1,1,3] => [3,1,1] => 1
[1,3,2,5,4,6] => 10101 => [1,1,1,1,1] => [1,1,1,1,1] => 1
[1,3,4,2,5,6] => 10011 => [1,2,2] => [2,1,2] => 2
[1,3,4,5,2,6] => 10001 => [1,3,1] => [1,1,3] => 3
[1,3,5,2,4,6] => 10001 => [1,3,1] => [1,1,3] => 3
[1,3,5,4,2,6] => 10001 => [1,3,1] => [1,1,3] => 3
[1,4,2,3,5,6] => 10011 => [1,2,2] => [2,1,2] => 2
[1,4,2,5,3,6] => 10001 => [1,3,1] => [1,1,3] => 3
[1,4,3,2,5,6] => 10011 => [1,2,2] => [2,1,2] => 2
[1,4,3,5,2,6] => 10001 => [1,3,1] => [1,1,3] => 3
[1,4,5,2,3,6] => 10001 => [1,3,1] => [1,1,3] => 3
[] => => [] => ? => ? = 1
Description
The last part of an integer composition.
Matching statistic: St001879
(load all 2 compositions to match this statistic)
Mapping
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00009: Binary trees —left rotate⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 83%
Values
[1] => [.,.]
 => [.,.]
 => ([],1)
 => ? = 1 + 1
[1,2] => [.,[.,.]]
 => [[.,.],.]
 => ([(0,1)],2)
 => ? = 1 + 1
[1,2,3] => [.,[.,[.,.]]]
 => [[.,.],[.,.]]
 => ([(0,2),(1,2)],3)
 => ? = 2 + 1
[2,1,3] => [[.,.],[.,.]]
 => [[[.,.],.],.]
 => ([(0,2),(2,1)],3)
 => 2 = 1 + 1
[1,2,3,4] => [.,[.,[.,[.,.]]]]
 => [[.,.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3 + 1
[1,3,2,4] => [.,[[.,.],[.,.]]]
 => [[.,[.,.]],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1 + 1
[2,1,3,4] => [[.,.],[.,[.,.]]]
 => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1 + 1
[2,3,1,4] => [[.,.],[.,[.,.]]]
 => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2 + 1
[3,1,2,4] => [[.,[.,.]],[.,.]]
 => [[[.,[.,.]],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 2 + 1
[3,2,1,4] => [[[.,.],.],[.,.]]
 => [[[[.,.],.],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 2 + 1
[1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
 => [[.,.],[.,[.,[.,.]]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4 + 1
[1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
 => [[.,.],[[.,.],[.,.]]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 1 + 1
[1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
 => [[.,[.,.]],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 1 + 1
[1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]]
 => [[.,[.,.]],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 2 + 1
[1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]]
 => [[.,[.,[.,.]]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 1
[1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
 => [[.,[[.,.],.]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 1
[2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
 => [[[.,.],.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 1 + 1
[2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
 => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 1 + 1
[2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]]
 => [[[.,.],.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 2 + 1
[2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]]
 => [[[.,.],.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 3 + 1
[2,4,1,3,5] => [[.,.],[[.,.],[.,.]]]
 => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 3 + 1
[2,4,3,1,5] => [[.,.],[[.,.],[.,.]]]
 => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 3 + 1
[3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]]
 => [[[.,[.,.]],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 1
[3,1,4,2,5] => [[.,[.,.]],[.,[.,.]]]
 => [[[.,[.,.]],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 3 + 1
[3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
 => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 1
[3,2,4,1,5] => [[[.,.],.],[.,[.,.]]]
 => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 3 + 1
[3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]]
 => [[[.,[.,.]],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 3 + 1
[3,4,2,1,5] => [[[.,.],.],[.,[.,.]]]
 => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 3 + 1
[4,1,2,3,5] => [[.,[.,[.,.]]],[.,.]]
 => [[[.,[.,[.,.]]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 3 + 1
[4,1,3,2,5] => [[.,[[.,.],.]],[.,.]]
 => [[[.,[[.,.],.]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 3 + 1
[4,2,1,3,5] => [[[.,.],[.,.]],[.,.]]
 => [[[[.,.],[.,.]],.],.]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3 + 1
[4,2,3,1,5] => [[[.,.],[.,.]],[.,.]]
 => [[[[.,.],[.,.]],.],.]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3 + 1
[4,3,1,2,5] => [[[.,[.,.]],.],[.,.]]
 => [[[[.,[.,.]],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 3 + 1
[4,3,2,1,5] => [[[[.,.],.],.],[.,.]]
 => [[[[[.,.],.],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 3 + 1
[1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
 => [[.,.],[.,[.,[.,[.,.]]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 5 + 1
[1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]]
 => [[.,.],[.,[[.,.],[.,.]]]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => ? = 1 + 1
[1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
 => [[.,.],[[.,.],[.,[.,.]]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 1 + 1
[1,2,4,5,3,6] => [.,[.,[[.,.],[.,[.,.]]]]]
 => [[.,.],[[.,.],[.,[.,.]]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 2 + 1
[1,2,5,3,4,6] => [.,[.,[[.,[.,.]],[.,.]]]]
 => [[.,.],[[.,[.,.]],[.,.]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 2 + 1
[1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]]
 => [[.,.],[[[.,.],.],[.,.]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 2 + 1
[1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]]
 => [[.,[.,.]],[.,[.,[.,.]]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 1 + 1
[1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]]
 => [[.,[.,.]],[[.,.],[.,.]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 1 + 1
[1,3,4,2,5,6] => [.,[[.,.],[.,[.,[.,.]]]]]
 => [[.,[.,.]],[.,[.,[.,.]]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 2 + 1
[1,3,4,5,2,6] => [.,[[.,.],[.,[.,[.,.]]]]]
 => [[.,[.,.]],[.,[.,[.,.]]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 3 + 1
[1,3,5,2,4,6] => [.,[[.,.],[[.,.],[.,.]]]]
 => [[.,[.,.]],[[.,.],[.,.]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,3,5,4,2,6] => [.,[[.,.],[[.,.],[.,.]]]]
 => [[.,[.,.]],[[.,.],[.,.]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,4,2,3,5,6] => [.,[[.,[.,.]],[.,[.,.]]]]
 => [[.,[.,[.,.]]],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 2 + 1
[1,4,2,5,3,6] => [.,[[.,[.,.]],[.,[.,.]]]]
 => [[.,[.,[.,.]]],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 3 + 1
[1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]]
 => [[.,[[.,.],.]],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 2 + 1
[1,4,3,5,2,6] => [.,[[[.,.],.],[.,[.,.]]]]
 => [[.,[[.,.],.]],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 3 + 1
[1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]]
 => [[.,[.,[.,.]]],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 3 + 1
[1,4,5,3,2,6] => [.,[[[.,.],.],[.,[.,.]]]]
 => [[.,[[.,.],.]],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 3 + 1
[1,5,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,.]]]
 => [[.,[.,[.,[.,.]]]],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 3 + 1
[1,5,2,4,3,6] => [.,[[.,[[.,.],.]],[.,.]]]
 => [[.,[.,[[.,.],.]]],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 3 + 1
[1,5,3,2,4,6] => [.,[[[.,.],[.,.]],[.,.]]]
 => [[.,[[.,.],[.,.]]],[.,.]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => ? = 3 + 1
[1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]]
 => [[.,[[.,.],[.,.]]],[.,.]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => ? = 3 + 1
[1,5,4,2,3,6] => [.,[[[.,[.,.]],.],[.,.]]]
 => [[.,[[.,[.,.]],.]],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 3 + 1
[5,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[.,.]]
 => [[[.,[.,[.,[.,.]]]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,1,2,4,3,6] => [[.,[.,[[.,.],.]]],[.,.]]
 => [[[.,[.,[[.,.],.]]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,1,4,2,3,6] => [[.,[[.,[.,.]],.]],[.,.]]
 => [[[.,[[.,[.,.]],.]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,1,4,3,2,6] => [[.,[[[.,.],.],.]],[.,.]]
 => [[[.,[[[.,.],.],.]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,4,1,2,3,6] => [[[.,[.,[.,.]]],.],[.,.]]
 => [[[[.,[.,[.,.]]],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,4,1,3,2,6] => [[[.,[[.,.],.]],.],[.,.]]
 => [[[[.,[[.,.],.]],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,4,3,1,2,6] => [[[[.,[.,.]],.],.],[.,.]]
 => [[[[[.,[.,.]],.],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]]
 => [[[[[[.,.],.],.],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[6,1,2,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
 => [[[.,[.,[.,[.,[.,.]]]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,2,3,5,4,7] => [[.,[.,[.,[[.,.],.]]]],[.,.]]
 => [[[.,[.,[.,[[.,.],.]]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,2,5,3,4,7] => [[.,[.,[[.,[.,.]],.]]],[.,.]]
 => [[[.,[.,[[.,[.,.]],.]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,2,5,4,3,7] => [[.,[.,[[[.,.],.],.]]],[.,.]]
 => [[[.,[.,[[[.,.],.],.]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,5,2,3,4,7] => [[.,[[.,[.,[.,.]]],.]],[.,.]]
 => [[[.,[[.,[.,[.,.]]],.]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,5,2,4,3,7] => [[.,[[.,[[.,.],.]],.]],[.,.]]
 => [[[.,[[.,[[.,.],.]],.]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,5,4,2,3,7] => [[.,[[[.,[.,.]],.],.]],[.,.]]
 => [[[.,[[[.,[.,.]],.],.]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,5,4,3,2,7] => [[.,[[[[.,.],.],.],.]],[.,.]]
 => [[[.,[[[[.,.],.],.],.]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,5,1,2,3,4,7] => [[[.,[.,[.,[.,.]]]],.],[.,.]]
 => [[[[.,[.,[.,[.,.]]]],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,5,1,2,4,3,7] => [[[.,[.,[[.,.],.]]],.],[.,.]]
 => [[[[.,[.,[[.,.],.]]],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,5,1,4,2,3,7] => [[[.,[[.,[.,.]],.]],.],[.,.]]
 => [[[[.,[[.,[.,.]],.]],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,5,1,4,3,2,7] => [[[.,[[[.,.],.],.]],.],[.,.]]
 => [[[[.,[[[.,.],.],.]],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,5,4,1,2,3,7] => [[[[.,[.,[.,.]]],.],.],[.,.]]
 => [[[[[.,[.,[.,.]]],.],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,5,4,1,3,2,7] => [[[[.,[[.,.],.]],.],.],[.,.]]
 => [[[[[.,[[.,.],.]],.],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,5,4,3,1,2,7] => [[[[[.,[.,.]],.],.],.],[.,.]]
 => [[[[[[.,[.,.]],.],.],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]]
 => [[[[[[[.,.],.],.],.],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
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
(load all 2 compositions to match this statistic)
Mapping
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00009: Binary trees —left rotate⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 83%
Values
[1] => [.,.]
 => [.,.]
 => ([],1)
 => ? = 1 + 2
[1,2] => [.,[.,.]]
 => [[.,.],.]
 => ([(0,1)],2)
 => ? = 1 + 2
[1,2,3] => [.,[.,[.,.]]]
 => [[.,.],[.,.]]
 => ([(0,2),(1,2)],3)
 => ? = 2 + 2
[2,1,3] => [[.,.],[.,.]]
 => [[[.,.],.],.]
 => ([(0,2),(2,1)],3)
 => 3 = 1 + 2
[1,2,3,4] => [.,[.,[.,[.,.]]]]
 => [[.,.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3 + 2
[1,3,2,4] => [.,[[.,.],[.,.]]]
 => [[.,[.,.]],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1 + 2
[2,1,3,4] => [[.,.],[.,[.,.]]]
 => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1 + 2
[2,3,1,4] => [[.,.],[.,[.,.]]]
 => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2 + 2
[3,1,2,4] => [[.,[.,.]],[.,.]]
 => [[[.,[.,.]],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 2 + 2
[3,2,1,4] => [[[.,.],.],[.,.]]
 => [[[[.,.],.],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 2 + 2
[1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
 => [[.,.],[.,[.,[.,.]]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4 + 2
[1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
 => [[.,.],[[.,.],[.,.]]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 1 + 2
[1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
 => [[.,[.,.]],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]]
 => [[.,[.,.]],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 2 + 2
[1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]]
 => [[.,[.,[.,.]]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 2
[1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
 => [[.,[[.,.],.]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 2
[2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
 => [[[.,.],.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 1 + 2
[2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
 => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 1 + 2
[2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]]
 => [[[.,.],.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 2 + 2
[2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]]
 => [[[.,.],.],[.,[.,.]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 3 + 2
[2,4,1,3,5] => [[.,.],[[.,.],[.,.]]]
 => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 3 + 2
[2,4,3,1,5] => [[.,.],[[.,.],[.,.]]]
 => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 3 + 2
[3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]]
 => [[[.,[.,.]],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 2
[3,1,4,2,5] => [[.,[.,.]],[.,[.,.]]]
 => [[[.,[.,.]],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 3 + 2
[3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
 => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 2
[3,2,4,1,5] => [[[.,.],.],[.,[.,.]]]
 => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 3 + 2
[3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]]
 => [[[.,[.,.]],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 3 + 2
[3,4,2,1,5] => [[[.,.],.],[.,[.,.]]]
 => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 3 + 2
[4,1,2,3,5] => [[.,[.,[.,.]]],[.,.]]
 => [[[.,[.,[.,.]]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 3 + 2
[4,1,3,2,5] => [[.,[[.,.],.]],[.,.]]
 => [[[.,[[.,.],.]],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 3 + 2
[4,2,1,3,5] => [[[.,.],[.,.]],[.,.]]
 => [[[[.,.],[.,.]],.],.]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3 + 2
[4,2,3,1,5] => [[[.,.],[.,.]],[.,.]]
 => [[[[.,.],[.,.]],.],.]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 3 + 2
[4,3,1,2,5] => [[[.,[.,.]],.],[.,.]]
 => [[[[.,[.,.]],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 3 + 2
[4,3,2,1,5] => [[[[.,.],.],.],[.,.]]
 => [[[[[.,.],.],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 3 + 2
[1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
 => [[.,.],[.,[.,[.,[.,.]]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 5 + 2
[1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]]
 => [[.,.],[.,[[.,.],[.,.]]]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => ? = 1 + 2
[1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
 => [[.,.],[[.,.],[.,[.,.]]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 1 + 2
[1,2,4,5,3,6] => [.,[.,[[.,.],[.,[.,.]]]]]
 => [[.,.],[[.,.],[.,[.,.]]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 2 + 2
[1,2,5,3,4,6] => [.,[.,[[.,[.,.]],[.,.]]]]
 => [[.,.],[[.,[.,.]],[.,.]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 2 + 2
[1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]]
 => [[.,.],[[[.,.],.],[.,.]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 2 + 2
[1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]]
 => [[.,[.,.]],[.,[.,[.,.]]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 1 + 2
[1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]]
 => [[.,[.,.]],[[.,.],[.,.]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 1 + 2
[1,3,4,2,5,6] => [.,[[.,.],[.,[.,[.,.]]]]]
 => [[.,[.,.]],[.,[.,[.,.]]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 2 + 2
[1,3,4,5,2,6] => [.,[[.,.],[.,[.,[.,.]]]]]
 => [[.,[.,.]],[.,[.,[.,.]]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 3 + 2
[1,3,5,2,4,6] => [.,[[.,.],[[.,.],[.,.]]]]
 => [[.,[.,.]],[[.,.],[.,.]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 3 + 2
[1,3,5,4,2,6] => [.,[[.,.],[[.,.],[.,.]]]]
 => [[.,[.,.]],[[.,.],[.,.]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 3 + 2
[1,4,2,3,5,6] => [.,[[.,[.,.]],[.,[.,.]]]]
 => [[.,[.,[.,.]]],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 2 + 2
[1,4,2,5,3,6] => [.,[[.,[.,.]],[.,[.,.]]]]
 => [[.,[.,[.,.]]],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 3 + 2
[1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]]
 => [[.,[[.,.],.]],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 2 + 2
[1,4,3,5,2,6] => [.,[[[.,.],.],[.,[.,.]]]]
 => [[.,[[.,.],.]],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 3 + 2
[1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]]
 => [[.,[.,[.,.]]],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 3 + 2
[1,4,5,3,2,6] => [.,[[[.,.],.],[.,[.,.]]]]
 => [[.,[[.,.],.]],[.,[.,.]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 3 + 2
[1,5,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,.]]]
 => [[.,[.,[.,[.,.]]]],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 3 + 2
[1,5,2,4,3,6] => [.,[[.,[[.,.],.]],[.,.]]]
 => [[.,[.,[[.,.],.]]],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 3 + 2
[1,5,3,2,4,6] => [.,[[[.,.],[.,.]],[.,.]]]
 => [[.,[[.,.],[.,.]]],[.,.]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => ? = 3 + 2
[1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]]
 => [[.,[[.,.],[.,.]]],[.,.]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => ? = 3 + 2
[1,5,4,2,3,6] => [.,[[[.,[.,.]],.],[.,.]]]
 => [[.,[[.,[.,.]],.]],[.,.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 3 + 2
[5,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[.,.]]
 => [[[.,[.,[.,[.,.]]]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,1,2,4,3,6] => [[.,[.,[[.,.],.]]],[.,.]]
 => [[[.,[.,[[.,.],.]]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,1,4,2,3,6] => [[.,[[.,[.,.]],.]],[.,.]]
 => [[[.,[[.,[.,.]],.]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,1,4,3,2,6] => [[.,[[[.,.],.],.]],[.,.]]
 => [[[.,[[[.,.],.],.]],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,4,1,2,3,6] => [[[.,[.,[.,.]]],.],[.,.]]
 => [[[[.,[.,[.,.]]],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,4,1,3,2,6] => [[[.,[[.,.],.]],.],[.,.]]
 => [[[[.,[[.,.],.]],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,4,3,1,2,6] => [[[[.,[.,.]],.],.],[.,.]]
 => [[[[[.,[.,.]],.],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]]
 => [[[[[[.,.],.],.],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[6,1,2,3,4,5,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
 => [[[.,[.,[.,[.,[.,.]]]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,2,3,5,4,7] => [[.,[.,[.,[[.,.],.]]]],[.,.]]
 => [[[.,[.,[.,[[.,.],.]]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,2,5,3,4,7] => [[.,[.,[[.,[.,.]],.]]],[.,.]]
 => [[[.,[.,[[.,[.,.]],.]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,2,5,4,3,7] => [[.,[.,[[[.,.],.],.]]],[.,.]]
 => [[[.,[.,[[[.,.],.],.]]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,5,2,3,4,7] => [[.,[[.,[.,[.,.]]],.]],[.,.]]
 => [[[.,[[.,[.,[.,.]]],.]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,5,2,4,3,7] => [[.,[[.,[[.,.],.]],.]],[.,.]]
 => [[[.,[[.,[[.,.],.]],.]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,5,4,2,3,7] => [[.,[[[.,[.,.]],.],.]],[.,.]]
 => [[[.,[[[.,[.,.]],.],.]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,5,4,3,2,7] => [[.,[[[[.,.],.],.],.]],[.,.]]
 => [[[.,[[[[.,.],.],.],.]],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,5,1,2,3,4,7] => [[[.,[.,[.,[.,.]]]],.],[.,.]]
 => [[[[.,[.,[.,[.,.]]]],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,5,1,2,4,3,7] => [[[.,[.,[[.,.],.]]],.],[.,.]]
 => [[[[.,[.,[[.,.],.]]],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,5,1,4,2,3,7] => [[[.,[[.,[.,.]],.]],.],[.,.]]
 => [[[[.,[[.,[.,.]],.]],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,5,1,4,3,2,7] => [[[.,[[[.,.],.],.]],.],[.,.]]
 => [[[[.,[[[.,.],.],.]],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,5,4,1,2,3,7] => [[[[.,[.,[.,.]]],.],.],[.,.]]
 => [[[[[.,[.,[.,.]]],.],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,5,4,1,3,2,7] => [[[[.,[[.,.],.]],.],.],[.,.]]
 => [[[[[.,[[.,.],.]],.],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,5,4,3,1,2,7] => [[[[[.,[.,.]],.],.],.],[.,.]]
 => [[[[[[.,[.,.]],.],.],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]]
 => [[[[[[[.,.],.],.],.],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.