Your data matches 4 different statistics following compositions of up to 3 maps.
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Matching statistic: St001382
(load all 2 compositions to match this statistic)
Mapping
St001382: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 0
[2]
 => 1
[1,1]
 => 1
[3]
 => 2
[2,1]
 => 2
[1,1,1]
 => 2
[4]
 => 3
[3,1]
 => 3
[2,2]
 => 0
[2,1,1]
 => 3
[1,1,1,1]
 => 3
[5]
 => 4
[4,1]
 => 4
[3,2]
 => 1
[3,1,1]
 => 4
[2,2,1]
 => 1
[2,1,1,1]
 => 4
[1,1,1,1,1]
 => 4
[6]
 => 5
[5,1]
 => 5
[4,2]
 => 2
[4,1,1]
 => 5
[3,3]
 => 2
[3,2,1]
 => 2
[3,1,1,1]
 => 5
[2,2,2]
 => 2
[2,2,1,1]
 => 2
[2,1,1,1,1]
 => 5
[1,1,1,1,1,1]
 => 5
[7]
 => 6
[6,1]
 => 6
[5,2]
 => 3
[5,1,1]
 => 6
[4,3]
 => 3
[4,2,1]
 => 3
[4,1,1,1]
 => 6
[3,3,1]
 => 3
[3,2,2]
 => 3
[3,2,1,1]
 => 3
[3,1,1,1,1]
 => 6
[2,2,2,1]
 => 3
[2,2,1,1,1]
 => 3
[2,1,1,1,1,1]
 => 6
[1,1,1,1,1,1,1]
 => 6
[8]
 => 7
[7,1]
 => 7
[6,2]
 => 4
[6,1,1]
 => 7
[5,3]
 => 4
[5,2,1]
 => 4
Description
The number of boxes in the diagram of a partition that do not lie in its Durfee square.
Matching statistic: St000921
(load all 4 compositions to match this statistic)
Mapping
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St000921: Binary words ⟶ ℤResult quality: 26% ●values known / values provided: 26%●distinct values known / distinct values provided: 52%
Values
[1]
 => [1]
 => 10 => 0
[2]
 => [1,1]
 => 110 => 1
[1,1]
 => [2]
 => 100 => 1
[3]
 => [1,1,1]
 => 1110 => 2
[2,1]
 => [2,1]
 => 1010 => 2
[1,1,1]
 => [3]
 => 1000 => 2
[4]
 => [1,1,1,1]
 => 11110 => 3
[3,1]
 => [2,1,1]
 => 10110 => 3
[2,2]
 => [2,2]
 => 1100 => 0
[2,1,1]
 => [3,1]
 => 10010 => 3
[1,1,1,1]
 => [4]
 => 10000 => 3
[5]
 => [1,1,1,1,1]
 => 111110 => 4
[4,1]
 => [2,1,1,1]
 => 101110 => 4
[3,2]
 => [2,2,1]
 => 11010 => 1
[3,1,1]
 => [3,1,1]
 => 100110 => 4
[2,2,1]
 => [3,2]
 => 10100 => 1
[2,1,1,1]
 => [4,1]
 => 100010 => 4
[1,1,1,1,1]
 => [5]
 => 100000 => 4
[6]
 => [1,1,1,1,1,1]
 => 1111110 => 5
[5,1]
 => [2,1,1,1,1]
 => 1011110 => 5
[4,2]
 => [2,2,1,1]
 => 110110 => 2
[4,1,1]
 => [3,1,1,1]
 => 1001110 => 5
[3,3]
 => [2,2,2]
 => 11100 => 2
[3,2,1]
 => [3,2,1]
 => 101010 => 2
[3,1,1,1]
 => [4,1,1]
 => 1000110 => 5
[2,2,2]
 => [3,3]
 => 11000 => 2
[2,2,1,1]
 => [4,2]
 => 100100 => 2
[2,1,1,1,1]
 => [5,1]
 => 1000010 => 5
[1,1,1,1,1,1]
 => [6]
 => 1000000 => 5
[7]
 => [1,1,1,1,1,1,1]
 => 11111110 => 6
[6,1]
 => [2,1,1,1,1,1]
 => 10111110 => 6
[5,2]
 => [2,2,1,1,1]
 => 1101110 => 3
[5,1,1]
 => [3,1,1,1,1]
 => 10011110 => 6
[4,3]
 => [2,2,2,1]
 => 111010 => 3
[4,2,1]
 => [3,2,1,1]
 => 1010110 => 3
[4,1,1,1]
 => [4,1,1,1]
 => 10001110 => 6
[3,3,1]
 => [3,2,2]
 => 101100 => 3
[3,2,2]
 => [3,3,1]
 => 110010 => 3
[3,2,1,1]
 => [4,2,1]
 => 1001010 => 3
[3,1,1,1,1]
 => [5,1,1]
 => 10000110 => 6
[2,2,2,1]
 => [4,3]
 => 101000 => 3
[2,2,1,1,1]
 => [5,2]
 => 1000100 => 3
[2,1,1,1,1,1]
 => [6,1]
 => 10000010 => 6
[1,1,1,1,1,1,1]
 => [7]
 => 10000000 => 6
[8]
 => [1,1,1,1,1,1,1,1]
 => 111111110 => 7
[7,1]
 => [2,1,1,1,1,1,1]
 => 101111110 => 7
[6,2]
 => [2,2,1,1,1,1]
 => 11011110 => 4
[6,1,1]
 => [3,1,1,1,1,1]
 => 100111110 => 7
[5,3]
 => [2,2,2,1,1]
 => 1110110 => 4
[5,2,1]
 => [3,2,1,1,1]
 => 10101110 => 4
[11]
 => [1,1,1,1,1,1,1,1,1,1,1]
 => 111111111110 => ? = 10
[10,1]
 => [2,1,1,1,1,1,1,1,1,1]
 => 101111111110 => ? = 10
[9,1,1]
 => [3,1,1,1,1,1,1,1,1]
 => 100111111110 => ? = 10
[8,1,1,1]
 => [4,1,1,1,1,1,1,1]
 => 100011111110 => ? = 10
[7,3,1]
 => [3,2,2,1,1,1,1]
 => 1011011110 => ? = 7
[7,2,2]
 => [3,3,1,1,1,1,1]
 => 1100111110 => ? = 7
[7,1,1,1,1]
 => [5,1,1,1,1,1,1]
 => 100001111110 => ? = 10
[6,3,1,1]
 => [4,2,2,1,1,1]
 => 1001101110 => ? = 7
[6,2,2,1]
 => [4,3,1,1,1,1]
 => 1010011110 => ? = 7
[6,1,1,1,1,1]
 => [6,1,1,1,1,1]
 => 100000111110 => ? = 10
[5,1,1,1,1,1,1]
 => [7,1,1,1,1]
 => 100000011110 => ? = 10
[4,3,1,1,1,1]
 => [6,2,2,1]
 => 1000011010 => ? = 7
[4,2,2,1,1,1]
 => [6,3,1,1]
 => 1000100110 => ? = 7
[4,1,1,1,1,1,1,1]
 => [8,1,1,1]
 => 100000001110 => ? = 10
[3,3,1,1,1,1,1]
 => [7,2,2]
 => 1000001100 => ? = 7
[3,2,2,1,1,1,1]
 => [7,3,1]
 => 1000010010 => ? = 7
[3,1,1,1,1,1,1,1,1]
 => [9,1,1]
 => 100000000110 => ? = 10
[2,2,2,1,1,1,1,1]
 => [8,3]
 => 1000001000 => ? = 7
[2,1,1,1,1,1,1,1,1,1]
 => [10,1]
 => 100000000010 => ? = 10
[1,1,1,1,1,1,1,1,1,1,1]
 => [11]
 => 100000000000 => ? = 10
[12]
 => [1,1,1,1,1,1,1,1,1,1,1,1]
 => 1111111111110 => ? = 11
[11,1]
 => [2,1,1,1,1,1,1,1,1,1,1]
 => 1011111111110 => ? = 11
[10,2]
 => [2,2,1,1,1,1,1,1,1,1]
 => 110111111110 => ? = 8
[10,1,1]
 => [3,1,1,1,1,1,1,1,1,1]
 => 1001111111110 => ? = 11
[9,3]
 => [2,2,2,1,1,1,1,1,1]
 => 11101111110 => ? = 8
[9,2,1]
 => [3,2,1,1,1,1,1,1,1]
 => 101011111110 => ? = 8
[9,1,1,1]
 => [4,1,1,1,1,1,1,1,1]
 => 1000111111110 => ? = 11
[8,4]
 => [2,2,2,2,1,1,1,1]
 => 1111011110 => ? = 8
[8,3,1]
 => [3,2,2,1,1,1,1,1]
 => 10110111110 => ? = 8
[8,2,2]
 => [3,3,1,1,1,1,1,1]
 => 11001111110 => ? = 8
[8,2,1,1]
 => [4,2,1,1,1,1,1,1]
 => 100101111110 => ? = 8
[8,1,1,1,1]
 => [5,1,1,1,1,1,1,1]
 => 1000011111110 => ? = 11
[7,4,1]
 => [3,2,2,2,1,1,1]
 => 1011101110 => ? = 8
[7,3,2]
 => [3,3,2,1,1,1,1]
 => 1101011110 => ? = 8
[7,3,1,1]
 => [4,2,2,1,1,1,1]
 => 10011011110 => ? = 8
[7,2,2,1]
 => [4,3,1,1,1,1,1]
 => 10100111110 => ? = 8
[7,2,1,1,1]
 => [5,2,1,1,1,1,1]
 => 100010111110 => ? = 8
[7,1,1,1,1,1]
 => [6,1,1,1,1,1,1]
 => 1000001111110 => ? = 11
[6,4,1,1]
 => [4,2,2,2,1,1]
 => 1001110110 => ? = 8
[6,3,2,1]
 => [4,3,2,1,1,1]
 => 1010101110 => ? = 8
[6,3,1,1,1]
 => [5,2,2,1,1,1]
 => 10001101110 => ? = 8
[6,2,2,2]
 => [4,4,1,1,1,1]
 => 1100011110 => ? = 8
[6,2,2,1,1]
 => [5,3,1,1,1,1]
 => 10010011110 => ? = 8
[6,2,1,1,1,1]
 => [6,2,1,1,1,1]
 => 100001011110 => ? = 8
[6,1,1,1,1,1,1]
 => [7,1,1,1,1,1]
 => 1000000111110 => ? = 11
[5,3,1,1,1,1]
 => [6,2,2,1,1]
 => 10000110110 => ? = 8
[5,2,2,1,1,1]
 => [6,3,1,1,1]
 => 10001001110 => ? = 8
[5,2,1,1,1,1,1]
 => [7,2,1,1,1]
 => 100000101110 => ? = 8
[5,1,1,1,1,1,1,1]
 => [8,1,1,1,1]
 => 1000000011110 => ? = 11
[4,4,1,1,1,1]
 => [6,2,2,2]
 => 1000011100 => ? = 8
Description
The number of internal inversions of a binary word. Let $\bar w$ be the non-decreasing rearrangement of $w$, that is, $\bar w$ is sorted. An internal inversion is a pair $i < j$ such that $w_i > w_j$ and $\bar w_i = \bar w_j$. For example, the word $110$ has two inversions, but only the second is internal.
Matching statistic: St001879
Mapping
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00140: Dyck paths —logarithmic height to pruning number⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 20%
Values
[1]
 => [1,0]
 => [.,.]
 => ([],1)
 => ? = 0
[2]
 => [1,0,1,0]
 => [.,[.,.]]
 => ([(0,1)],2)
 => ? = 1
[1,1]
 => [1,1,0,0]
 => [[.,.],.]
 => ([(0,1)],2)
 => ? = 1
[3]
 => [1,0,1,0,1,0]
 => [.,[.,[.,.]]]
 => ([(0,2),(2,1)],3)
 => 2
[2,1]
 => [1,0,1,1,0,0]
 => [.,[[.,.],.]]
 => ([(0,2),(2,1)],3)
 => 2
[1,1,1]
 => [1,1,0,1,0,0]
 => [[[.,.],.],.]
 => ([(0,2),(2,1)],3)
 => 2
[4]
 => [1,0,1,0,1,0,1,0]
 => [.,[.,[.,[.,.]]]]
 => ([(0,3),(2,1),(3,2)],4)
 => 3
[3,1]
 => [1,0,1,0,1,1,0,0]
 => [.,[.,[[.,.],.]]]
 => ([(0,3),(2,1),(3,2)],4)
 => 3
[2,2]
 => [1,1,1,0,0,0]
 => [[.,.],[.,.]]
 => ([(0,2),(1,2)],3)
 => ? = 0
[2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [.,[[[.,.],.],.]]
 => ([(0,3),(2,1),(3,2)],4)
 => 3
[1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [[[[.,.],.],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 3
[5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [.,[.,[.,[.,[.,.]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [.,[.,[.,[[.,.],.]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[3,2]
 => [1,0,1,1,1,0,0,0]
 => [.,[[.,.],[.,.]]]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 1
[3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [.,[.,[[[.,.],.],.]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1
[2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [.,[[[[.,.],.],.],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [[[[[.,.],.],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [.,[.,[.,[.,[.,[.,.]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [.,[.,[.,[.,[[.,.],.]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [.,[.,[[.,.],[.,.]]]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 2
[4,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [.,[.,[.,[[[.,.],.],.]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[3,3]
 => [1,1,1,0,1,0,0,0]
 => [[.,[.,.]],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2
[3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [.,[[.,.],[[.,.],.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 2
[3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [.,[.,[[[[.,.],.],.],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2
[2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2
[2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [[[[[[.,.],.],.],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [.,[.,[.,[.,[.,[.,[.,.]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[6,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [.,[.,[.,[.,[.,[[.,.],.]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [.,[.,[.,[[.,.],[.,.]]]]]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ? = 3
[5,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [.,[.,[.,[.,[[[.,.],.],.]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [.,[[.,[.,.]],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3
[4,2,1]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => [.,[.,[[.,.],[[.,.],.]]]]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 3
[4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [.,[.,[.,[[[[.,.],.],.],.]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => [[.,[.,.]],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 3
[3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [.,[[[.,.],.],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3
[3,2,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,0]
 => [.,[[.,.],[[[.,.],.],.]]]
 => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ? = 3
[3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [.,[.,[[[[[.,.],.],.],.],.]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => [[[.,.],.],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 3
[2,2,1,1,1]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [[.,.],[[[[.,.],.],.],.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 3
[2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [.,[[[[[[.,.],.],.],.],.],.]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [[[[[[[.,.],.],.],.],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6
[8]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 7
[7,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 7
[6,2]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [.,[.,[.,[.,[[.,.],[.,.]]]]]]
 => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
 => ? = 4
[6,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 7
[5,3]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => [.,[.,[[.,[.,.]],[.,.]]]]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 4
[5,2,1]
 => [1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [.,[.,[.,[[.,.],[[.,.],.]]]]]
 => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
 => ? = 4
[5,1,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 7
[4,4]
 => [1,1,1,0,1,0,1,0,0,0]
 => [[.,[.,[.,.]]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4
[4,3,1]
 => [1,0,1,1,1,0,1,0,0,1,0,0]
 => [.,[[.,[.,.]],[[.,.],.]]]
 => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => ? = 4
[4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [.,[.,[[[.,.],.],[.,.]]]]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 4
[4,2,1,1]
 => [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [.,[.,[[.,.],[[[.,.],.],.]]]]
 => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
 => ? = 4
[4,1,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [.,[.,[.,[[[[[.,.],.],.],.],.]]]]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 7
[3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => [[.,[[.,.],.]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4
[3,3,1,1]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [[.,[.,.]],[[[.,.],.],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 4
[3,2,2,1]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [.,[[[.,.],.],[[.,.],.]]]
 => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => ? = 4
[3,2,1,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,1,0,0]
 => [.,[[.,.],[[[[.,.],.],.],.]]]
 => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => ? = 4
[3,1,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [.,[.,[[[[[[.,.],.],.],.],.],.]]]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 7
[2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4
[2,2,2,1,1]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [[[.,.],.],[[[.,.],.],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 4
[2,2,1,1,1,1]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => [[.,.],[[[[[.,.],.],.],.],.]]
 => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
 => ? = 4
[2,1,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [.,[[[[[[[.,.],.],.],.],.],.],.]]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 7
[1,1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [[[[[[[[.,.],.],.],.],.],.],.],.]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 7
[9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
 => ? = 8
[8,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
 => ? = 8
[7,2]
 => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
 => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
 => ? = 5
[7,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
 => ? = 8
[6,3]
 => [1,0,1,0,1,0,1,1,1,0,1,0,0,0]
 => [.,[.,[.,[[.,[.,.]],[.,.]]]]]
 => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
 => ? = 5
[6,2,1]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
 => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
 => ? = 5
[6,1,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
 => ? = 8
[5,4]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [.,[[.,[.,[.,.]]],[.,.]]]
 => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ? = 5
[5,3,1]
 => [1,0,1,0,1,1,1,0,1,0,0,1,0,0]
 => [.,[.,[[.,[.,.]],[[.,.],.]]]]
 => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
 => ? = 5
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
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00140: Dyck paths —logarithmic height to pruning number⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 20%
Values
[1]
 => [1,0]
 => [.,.]
 => ([],1)
 => ? = 0 + 1
[2]
 => [1,0,1,0]
 => [.,[.,.]]
 => ([(0,1)],2)
 => ? = 1 + 1
[1,1]
 => [1,1,0,0]
 => [[.,.],.]
 => ([(0,1)],2)
 => ? = 1 + 1
[3]
 => [1,0,1,0,1,0]
 => [.,[.,[.,.]]]
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
[2,1]
 => [1,0,1,1,0,0]
 => [.,[[.,.],.]]
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
[1,1,1]
 => [1,1,0,1,0,0]
 => [[[.,.],.],.]
 => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
[4]
 => [1,0,1,0,1,0,1,0]
 => [.,[.,[.,[.,.]]]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[3,1]
 => [1,0,1,0,1,1,0,0]
 => [.,[.,[[.,.],.]]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[2,2]
 => [1,1,1,0,0,0]
 => [[.,.],[.,.]]
 => ([(0,2),(1,2)],3)
 => ? = 0 + 1
[2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [.,[[[.,.],.],.]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [[[[.,.],.],.],.]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [.,[.,[.,[.,[.,.]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [.,[.,[.,[[.,.],.]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[3,2]
 => [1,0,1,1,1,0,0,0]
 => [.,[[.,.],[.,.]]]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 1 + 1
[3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [.,[.,[[[.,.],.],.]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1 + 1
[2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [.,[[[[.,.],.],.],.]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [[[[[.,.],.],.],.],.]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [.,[.,[.,[.,[.,[.,.]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [.,[.,[.,[.,[[.,.],.]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [.,[.,[[.,.],[.,.]]]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 2 + 1
[4,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [.,[.,[.,[[[.,.],.],.]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[3,3]
 => [1,1,1,0,1,0,0,0]
 => [[.,[.,.]],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2 + 1
[3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [.,[[.,.],[[.,.],.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 2 + 1
[3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [.,[.,[[[[.,.],.],.],.]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2 + 1
[2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 1
[2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [[[[[[.,.],.],.],.],.],.]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [.,[.,[.,[.,[.,[.,[.,.]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[6,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [.,[.,[.,[.,[.,[[.,.],.]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[5,2]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [.,[.,[.,[[.,.],[.,.]]]]]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ? = 3 + 1
[5,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [.,[.,[.,[.,[[[.,.],.],.]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [.,[[.,[.,.]],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3 + 1
[4,2,1]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => [.,[.,[[.,.],[[.,.],.]]]]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 3 + 1
[4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [.,[.,[.,[[[[.,.],.],.],.]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => [[.,[.,.]],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 3 + 1
[3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [.,[[[.,.],.],[.,.]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3 + 1
[3,2,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,0]
 => [.,[[.,.],[[[.,.],.],.]]]
 => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ? = 3 + 1
[3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [.,[.,[[[[[.,.],.],.],.],.]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => [[[.,.],.],[[.,.],.]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 3 + 1
[2,2,1,1,1]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [[.,.],[[[[.,.],.],.],.]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 3 + 1
[2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [.,[[[[[[.,.],.],.],.],.],.]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [[[[[[[.,.],.],.],.],.],.],.]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 6 + 1
[8]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 7 + 1
[7,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 7 + 1
[6,2]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [.,[.,[.,[.,[[.,.],[.,.]]]]]]
 => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
 => ? = 4 + 1
[6,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 7 + 1
[5,3]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => [.,[.,[[.,[.,.]],[.,.]]]]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 4 + 1
[5,2,1]
 => [1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [.,[.,[.,[[.,.],[[.,.],.]]]]]
 => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
 => ? = 4 + 1
[5,1,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 7 + 1
[4,4]
 => [1,1,1,0,1,0,1,0,0,0]
 => [[.,[.,[.,.]]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4 + 1
[4,3,1]
 => [1,0,1,1,1,0,1,0,0,1,0,0]
 => [.,[[.,[.,.]],[[.,.],.]]]
 => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => ? = 4 + 1
[4,2,2]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [.,[.,[[[.,.],.],[.,.]]]]
 => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => ? = 4 + 1
[4,2,1,1]
 => [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [.,[.,[[.,.],[[[.,.],.],.]]]]
 => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
 => ? = 4 + 1
[4,1,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [.,[.,[.,[[[[[.,.],.],.],.],.]]]]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 7 + 1
[3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => [[.,[[.,.],.]],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4 + 1
[3,3,1,1]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [[.,[.,.]],[[[.,.],.],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 4 + 1
[3,2,2,1]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [.,[[[.,.],.],[[.,.],.]]]
 => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => ? = 4 + 1
[3,2,1,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,1,0,0]
 => [.,[[.,.],[[[[.,.],.],.],.]]]
 => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => ? = 4 + 1
[3,1,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [.,[.,[[[[[[.,.],.],.],.],.],.]]]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 7 + 1
[2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 4 + 1
[2,2,2,1,1]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [[[.,.],.],[[[.,.],.],.]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ? = 4 + 1
[2,2,1,1,1,1]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => [[.,.],[[[[[.,.],.],.],.],.]]
 => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
 => ? = 4 + 1
[2,1,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [.,[[[[[[[.,.],.],.],.],.],.],.]]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 7 + 1
[1,1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [[[[[[[[.,.],.],.],.],.],.],.],.]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 7 + 1
[9]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
 => ? = 8 + 1
[8,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
 => ? = 8 + 1
[7,2]
 => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
 => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
 => ? = 5 + 1
[7,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
 => ? = 8 + 1
[6,3]
 => [1,0,1,0,1,0,1,1,1,0,1,0,0,0]
 => [.,[.,[.,[[.,[.,.]],[.,.]]]]]
 => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
 => ? = 5 + 1
[6,2,1]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
 => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
 => ? = 5 + 1
[6,1,1,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
 => ? = 8 + 1
[5,4]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [.,[[.,[.,[.,.]]],[.,.]]]
 => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => ? = 5 + 1
[5,3,1]
 => [1,0,1,0,1,1,1,0,1,0,0,1,0,0]
 => [.,[.,[[.,[.,.]],[[.,.],.]]]]
 => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
 => ? = 5 + 1
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.