Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000815
Mp00127: Permutations left-to-right-maxima to Dyck pathDyck paths
Mp00233: Dyck paths skew partitionSkew partitions
Mp00183: Skew partitions inner shapeInteger partitions
St000815: Integer partitions ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
[2,1,3,4] => [1,1,0,0,1,0,1,0]
=> [[2,2,2],[1,1]]
=> [1,1]
=> 1
[2,3,1,4] => [1,1,0,1,0,0,1,0]
=> [[3,3],[2]]
=> [2]
=> 2
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1],[1,1]]
=> [1,1]
=> 1
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
=> [[3,3,1],[2]]
=> [2]
=> 2
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
=> [[2,2,2,2],[1,1,1]]
=> [1,1,1]
=> 1
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2],[1,1]]
=> [1,1]
=> 1
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2],[2,1]]
=> [2,1]
=> 3
[2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2],[1,1]]
=> [1,1]
=> 1
[2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2],[1,1]]
=> [1,1]
=> 1
[2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0]
=> [[3,3,3],[2,2]]
=> [2,2]
=> 4
[2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0]
=> [[4,3],[2]]
=> [2]
=> 2
[2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0]
=> [[4,4],[3]]
=> [3]
=> 3
[2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0]
=> [[4,4],[2]]
=> [2]
=> 2
[2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0]
=> [[4,4],[2]]
=> [2]
=> 2
[2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3],[2,1]]
=> [2,1]
=> 3
[2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3],[2,1]]
=> [2,1]
=> 3
[2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0]
=> [[3,3,3],[1,1]]
=> [1,1]
=> 1
[2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0]
=> [[3,3,3],[1,1]]
=> [1,1]
=> 1
[3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
=> [[2,2,2,2],[1,1]]
=> [1,1]
=> 1
[3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2],[2]]
=> [2]
=> 2
[3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
=> [[2,2,2,2],[1,1]]
=> [1,1]
=> 1
[3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2],[2]]
=> [2]
=> 2
[4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3],[2]]
=> [2]
=> 2
[4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3],[2]]
=> [2]
=> 2
[4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3],[2]]
=> [2]
=> 2
[4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3],[2]]
=> [2]
=> 2
[4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3],[2]]
=> [2]
=> 2
[4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3],[2]]
=> [2]
=> 2
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1,1],[1,1]]
=> [1,1]
=> 1
[1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0]
=> [[3,3,1,1],[2]]
=> [2]
=> 2
[1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [[2,2,2,2,1],[1,1,1]]
=> [1,1,1]
=> 1
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2,1],[1,1]]
=> [1,1]
=> 1
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2,1],[2,1]]
=> [2,1]
=> 3
[1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2,1],[1,1]]
=> [1,1]
=> 1
[1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2,1],[1,1]]
=> [1,1]
=> 1
[1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0]
=> [[3,3,3,1],[2,2]]
=> [2,2]
=> 4
[1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0]
=> [[4,3,1],[2]]
=> [2]
=> 2
[1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0]
=> [[4,4,1],[3]]
=> [3]
=> 3
[1,3,4,6,2,5] => [1,0,1,1,0,1,0,1,1,0,0,0]
=> [[4,4,1],[2]]
=> [2]
=> 2
[1,3,4,6,5,2] => [1,0,1,1,0,1,0,1,1,0,0,0]
=> [[4,4,1],[2]]
=> [2]
=> 2
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3,1],[2,1]]
=> [2,1]
=> 3
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3,1],[2,1]]
=> [2,1]
=> 3
[1,3,5,6,2,4] => [1,0,1,1,0,1,1,0,1,0,0,0]
=> [[3,3,3,1],[1,1]]
=> [1,1]
=> 1
[1,3,5,6,4,2] => [1,0,1,1,0,1,1,0,1,0,0,0]
=> [[3,3,3,1],[1,1]]
=> [1,1]
=> 1
[1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
=> [[2,2,2,2,1],[1,1]]
=> [1,1]
=> 1
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2,1],[2]]
=> [2]
=> 2
[1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
=> [[2,2,2,2,1],[1,1]]
=> [1,1]
=> 1
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2,1],[2]]
=> [2]
=> 2
[1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3,1],[2]]
=> [2]
=> 2
[1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3,1],[2]]
=> [2]
=> 2
Description
The number of semistandard Young tableaux of partition weight of given shape. The weight of a semistandard Young tableaux is the sequence $(m_1, m_2,\dots)$, where $m_i$ is the number of occurrences of the number $i$ in the tableau. This statistic counts those tableaux whose weight is a weakly decreasing sequence. Alternatively, this is the sum of the entries in the column specified by the partition of the change of basis matrix from Schur functions to monomial symmetric functions.
Mp00127: Permutations left-to-right-maxima to Dyck pathDyck paths
Mp00103: Dyck paths peeling mapDyck paths
St001232: Dyck paths ⟶ ℤResult quality: 2% values known / values provided: 2%distinct values known / distinct values provided: 2%
Values
[2,1,3,4] => [1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> ? = 1 + 5
[2,3,1,4] => [1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> ? = 2 + 5
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 5
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 5
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 5
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 5
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 3 + 5
[2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 5
[2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 5
[2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 4 + 5
[2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 5
[2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 3 + 5
[2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 5
[2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 5
[2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 3 + 5
[2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 3 + 5
[2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 5
[2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 5
[3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 5
[3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 5
[3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 5
[3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 5
[4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 2 + 5
[4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 2 + 5
[4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 2 + 5
[4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 2 + 5
[4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 2 + 5
[4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 2 + 5
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 5
[1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 5
[1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 5
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 5
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 3 + 5
[1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 5
[1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 5
[1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 4 + 5
[1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 5
[1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 3 + 5
[1,3,4,6,2,5] => [1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 5
[1,3,4,6,5,2] => [1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 5
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 3 + 5
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 3 + 5
[1,3,5,6,2,4] => [1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 5
[1,3,5,6,4,2] => [1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 5
[1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 5
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 5
[1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 5
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 5
[1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> ? = 2 + 5
[1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> ? = 2 + 5
[4,1,7,2,3,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,2,3,6,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,2,5,3,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,2,5,6,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,2,6,3,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,2,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,3,2,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,3,2,6,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,3,5,2,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,3,5,6,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,3,6,2,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,3,6,5,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,5,2,3,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,5,2,6,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,5,3,2,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,5,3,6,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,5,6,2,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,5,6,3,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,6,2,3,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,6,2,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,6,3,2,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,6,3,5,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,6,5,2,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,1,7,6,5,3,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,1,3,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,1,3,6,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,1,5,3,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,1,5,6,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,1,6,3,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,3,1,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,3,1,6,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,3,5,1,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,3,5,6,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,3,6,1,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,3,6,5,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,5,1,3,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,5,1,6,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,5,3,1,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,5,3,6,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,5,6,1,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,5,6,3,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,6,1,3,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,6,1,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,6,3,1,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,6,3,5,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,6,5,1,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,2,7,6,5,3,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,3,7,1,2,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
[4,3,7,1,2,6,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> 6 = 1 + 5
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.