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Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St000770
Mp00007: Alternating sign matrices —to Dyck path⟶ Dyck paths
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
St000770: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
St000770: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
=> [1,1,0,0,1,0,1,0]
=> [[2,2,2],[1,1]]
=> [1,1]
=> 1
[[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
=> [1,1,0,1,0,0,1,0]
=> [[3,3],[2]]
=> [2]
=> 2
[[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]]
=> [1,1,0,1,0,0,1,0]
=> [[3,3],[2]]
=> [2]
=> 2
[[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [1,1,0,0,1,0,1,0,1,0]
=> [[2,2,2,2],[1,1,1]]
=> [1,1,1]
=> 1
[[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1],[1,1]]
=> [1,1]
=> 1
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [1,1,0,1,0,0,1,0,1,0]
=> [[3,3,3],[2,2]]
=> [2,2]
=> 2
[[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [1,1,1,0,0,0,1,0,1,0]
=> [[2,2,2,2],[1,1]]
=> [1,1]
=> 1
[[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [1,1,0,1,0,0,1,0,1,0]
=> [[3,3,3],[2,2]]
=> [2,2]
=> 2
[[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [1,1,1,0,0,0,1,0,1,0]
=> [[2,2,2,2],[1,1]]
=> [1,1]
=> 1
[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2],[2,1]]
=> [2,1]
=> 4
[[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,0,1,1,0,1,0,0,1,0]
=> [[3,3,1],[2]]
=> [2]
=> 2
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,0,1,0,1,0,0,1,0]
=> [[4,4],[3]]
=> [3]
=> 3
[[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2],[2]]
=> [2]
=> 2
[[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,0,1,0,1,0,0,1,0]
=> [[4,4],[3]]
=> [3]
=> 3
[[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2],[2]]
=> [2]
=> 2
[[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3],[2,1]]
=> [2,1]
=> 4
[[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3],[2]]
=> [2]
=> 2
[[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3],[2,1]]
=> [2,1]
=> 4
[[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3],[2]]
=> [2]
=> 2
[[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,0,1,1,0,1,0,0,1,0]
=> [[3,3,1],[2]]
=> [2]
=> 2
[[0,1,0,0,0],[1,-1,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,0,1,0,1,0,0,1,0]
=> [[4,4],[3]]
=> [3]
=> 3
[[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2],[2]]
=> [2]
=> 2
[[0,1,0,0,0],[0,0,1,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,0,1,0,1,0,0,1,0]
=> [[4,4],[3]]
=> [3]
=> 3
[[0,0,1,0,0],[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2],[2]]
=> [2]
=> 2
[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3],[2,1]]
=> [2,1]
=> 4
[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3],[2]]
=> [2]
=> 2
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3],[2,1]]
=> [2,1]
=> 4
[[0,0,0,1,0],[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3],[2]]
=> [2]
=> 2
[[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3],[2]]
=> [2]
=> 2
[[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [1,1,0,1,0,1,0,0,1,0]
=> [[4,4],[3]]
=> [3]
=> 3
[[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2],[2]]
=> [2]
=> 2
[[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3],[2,1]]
=> [2,1]
=> 4
[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3],[2]]
=> [2]
=> 2
[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3],[2]]
=> [2]
=> 2
[[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2],[1,1]]
=> [1,1]
=> 1
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [1,1,0,1,0,0,1,1,0,0]
=> [[4,3],[2]]
=> [2]
=> 2
[[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [1,1,0,1,0,0,1,1,0,0]
=> [[4,3],[2]]
=> [2]
=> 2
[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
=> [1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2],[1,1]]
=> [1,1]
=> 1
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]
=> [1,1,0,1,0,1,1,0,0,0]
=> [[4,4],[2]]
=> [2]
=> 2
[[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]
=> [1,1,0,1,0,1,1,0,0,0]
=> [[4,4],[2]]
=> [2]
=> 2
[[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,0]
=> [[3,3,3],[1,1]]
=> [1,1]
=> 1
[[0,1,0,0,0],[0,0,0,1,0],[1,0,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,0]
=> [[3,3,3],[1,1]]
=> [1,1]
=> 1
[[0,1,0,0,0],[1,-1,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,1,0,1,0,1,1,0,0,0]
=> [[4,4],[2]]
=> [2]
=> 2
[[0,1,0,0,0],[0,0,1,0,0],[1,-1,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,1,0,1,0,1,1,0,0,0]
=> [[4,4],[2]]
=> [2]
=> 2
[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,-1,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,0]
=> [[3,3,3],[1,1]]
=> [1,1]
=> 1
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,-1,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,0]
=> [[3,3,3],[1,1]]
=> [1,1]
=> 1
[[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0]]
=> [1,1,0,1,0,1,1,0,0,0]
=> [[4,4],[2]]
=> [2]
=> 2
[[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[1,0,0,0,0],[0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,0]
=> [[3,3,3],[1,1]]
=> [1,1]
=> 1
[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2],[1,1]]
=> [1,1]
=> 1
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [1,1,0,1,0,1,1,0,0,0]
=> [[4,4],[2]]
=> [2]
=> 2
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
Mp00007: Alternating sign matrices —to Dyck path⟶ Dyck paths
Mp00229: Dyck paths —Delest-Viennot⟶ Dyck paths
Mp00103: Dyck paths —peeling map⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 12%
Mp00229: Dyck paths —Delest-Viennot⟶ Dyck paths
Mp00103: Dyck paths —peeling map⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 12%
Values
[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
=> [1,1,0,0,1,0,1,0]
=> [1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? = 1 + 4
[[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
=> [1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? = 2 + 4
[[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]]
=> [1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? = 2 + 4
[[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 4
[[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 4
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 4
[[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 4
[[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 4
[[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 4
[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 4 + 4
[[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 4
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 3 + 4
[[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 4
[[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 3 + 4
[[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 4
[[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 4 + 4
[[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 4
[[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 4 + 4
[[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 4
[[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 4
[[0,1,0,0,0],[1,-1,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 3 + 4
[[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 4
[[0,1,0,0,0],[0,0,1,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 3 + 4
[[0,0,1,0,0],[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 4
[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 4 + 4
[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 4
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 4 + 4
[[0,0,0,1,0],[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 4
[[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 4
[[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 3 + 4
[[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 4
[[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 4 + 4
[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 4
[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 4
[[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [1,1,0,0,1,0,1,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 4
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 4
[[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 4
[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 4
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 2 + 4
[[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 2 + 4
[[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 1 + 4
[[0,1,0,0,0],[0,0,0,1,0],[1,0,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 1 + 4
[[0,1,0,0,0],[1,-1,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 2 + 4
[[0,1,0,0,0],[0,0,1,0,0],[1,-1,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 2 + 4
[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,-1,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 1 + 4
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,-1,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 1 + 4
[[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0]]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 2 + 4
[[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[1,0,0,0,0],[0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 1 + 4
[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 4
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 2 + 4
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,0,0,0,0,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,-1,1,0],[0,0,0,1,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,-1,0,1,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,-1,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[1,0,0,0,-1,1],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,0,-1,1],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,-1,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,0,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,1,0,-1,0,1],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,-1,1,0],[0,0,0,1,0,0],[0,1,0,-1,0,1],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,-1,0,1,0,0],[0,1,0,-1,0,1],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,0,0,1,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,-1,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[1,0,0,-1,0,1],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[1,0,0,-1,0,1],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[1,0,-1,1,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0]]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5 = 1 + 4
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001645
Mp00007: Alternating sign matrices —to Dyck path⟶ Dyck paths
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 12%
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 12%
Values
[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
=> [1,1,0,0,1,0,1,0]
=> [2,1,3,4] => ([(2,3)],4)
=> ? = 1 + 28
[[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
=> [1,1,0,1,0,0,1,0]
=> [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? = 2 + 28
[[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]]
=> [1,1,0,1,0,0,1,0]
=> [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? = 2 + 28
[[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [1,1,0,0,1,0,1,0,1,0]
=> [2,1,3,4,5] => ([(3,4)],5)
=> ? = 1 + 28
[[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,3,2,4,5] => ([(3,4)],5)
=> ? = 1 + 28
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [1,1,0,1,0,0,1,0,1,0]
=> [2,3,1,4,5] => ([(2,4),(3,4)],5)
=> ? = 2 + 28
[[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [1,1,1,0,0,0,1,0,1,0]
=> [3,1,2,4,5] => ([(2,4),(3,4)],5)
=> ? = 1 + 28
[[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [1,1,0,1,0,0,1,0,1,0]
=> [2,3,1,4,5] => ([(2,4),(3,4)],5)
=> ? = 2 + 28
[[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [1,1,1,0,0,0,1,0,1,0]
=> [3,1,2,4,5] => ([(2,4),(3,4)],5)
=> ? = 1 + 28
[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,5] => ([(1,4),(2,3)],5)
=> ? = 4 + 28
[[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,3,4,2,5] => ([(2,4),(3,4)],5)
=> ? = 2 + 28
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 + 28
[[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,1,0,0,1,0,0,1,0]
=> [3,1,4,2,5] => ([(1,4),(2,3),(3,4)],5)
=> ? = 2 + 28
[[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 + 28
[[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,1,0,0,1,0,0,1,0]
=> [3,1,4,2,5] => ([(1,4),(2,3),(3,4)],5)
=> ? = 2 + 28
[[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,0,1,1,0,0,0,1,0]
=> [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5)
=> ? = 4 + 28
[[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 + 28
[[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,0,1,1,0,0,0,1,0]
=> [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5)
=> ? = 4 + 28
[[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 + 28
[[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,3,4,2,5] => ([(2,4),(3,4)],5)
=> ? = 2 + 28
[[0,1,0,0,0],[1,-1,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 + 28
[[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,1,0,0,1,0,0,1,0]
=> [3,1,4,2,5] => ([(1,4),(2,3),(3,4)],5)
=> ? = 2 + 28
[[0,1,0,0,0],[0,0,1,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 + 28
[[0,0,1,0,0],[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,1,0,0,1,0,0,1,0]
=> [3,1,4,2,5] => ([(1,4),(2,3),(3,4)],5)
=> ? = 2 + 28
[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,0,1,1,0,0,0,1,0]
=> [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5)
=> ? = 4 + 28
[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 + 28
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,0,1,1,0,0,0,1,0]
=> [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5)
=> ? = 4 + 28
[[0,0,0,1,0],[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 + 28
[[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 + 28
[[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 + 28
[[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [1,1,1,0,0,1,0,0,1,0]
=> [3,1,4,2,5] => ([(1,4),(2,3),(3,4)],5)
=> ? = 2 + 28
[[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [1,1,0,1,1,0,0,0,1,0]
=> [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5)
=> ? = 4 + 28
[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 + 28
[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [1,1,1,1,0,0,0,0,1,0]
=> [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 + 28
[[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [1,1,0,0,1,0,1,1,0,0]
=> [2,1,3,5,4] => ([(1,4),(2,3)],5)
=> ? = 1 + 28
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [1,1,0,1,0,0,1,1,0,0]
=> [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5)
=> ? = 2 + 28
[[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
=> [1,1,0,1,0,0,1,1,0,0]
=> [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5)
=> ? = 2 + 28
[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
=> [1,1,0,0,1,1,1,0,0,0]
=> [2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5)
=> ? = 1 + 28
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]
=> [1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 2 + 28
[[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]
=> [1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 2 + 28
[[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,0]
=> [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? = 1 + 28
[[0,1,0,0,0],[0,0,0,1,0],[1,0,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,0]
=> [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? = 1 + 28
[[0,1,0,0,0],[1,-1,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 2 + 28
[[0,1,0,0,0],[0,0,1,0,0],[1,-1,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 2 + 28
[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,-1,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,0]
=> [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? = 1 + 28
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,-1,1],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,0]
=> [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? = 1 + 28
[[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0]]
=> [1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 2 + 28
[[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[1,0,0,0,0],[0,0,0,1,0]]
=> [1,1,0,1,1,0,1,0,0,0]
=> [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ? = 1 + 28
[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [1,1,0,0,1,1,1,0,0,0]
=> [2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5)
=> ? = 1 + 28
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 2 + 28
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,-1,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,-1,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,1,-1,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,-1,0,0,1],[0,0,1,0,0,0],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,-1,0,0,0,1],[0,1,0,0,0,0],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,0,1,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,-1,0,0,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,1,-1,0,0,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,-1,0,0,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,0,0,0,0,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,-1,0,0,0,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[1,0,0,-1,1,0],[0,0,0,1,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,1,0,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,1,0,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,-1,0,0,1],[0,0,0,0,1,0],[0,0,1,0,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,1,-1,0,0,1],[0,0,0,0,1,0],[0,0,1,0,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,-1,0,0,1],[0,0,0,0,1,0],[0,0,1,0,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,1,-1,0,1,0],[0,0,1,0,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,0,0,0,0,1],[0,1,-1,0,1,0],[0,0,1,0,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,-1,0,0,0,1],[0,1,-1,0,1,0],[0,0,1,0,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[1,0,-1,0,1,0],[0,0,1,0,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[1,-1,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,-1,0,0,0,1],[0,0,0,0,1,0],[0,1,0,0,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[1,-1,0,0,1,0],[0,1,0,0,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
[[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[1,0,0,0,0,0]]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> 32 = 4 + 28
Description
The pebbling number of a connected graph.
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