Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000714
Mapping
Mp00079: Set partitions —shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000714: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1},{2},{3},{4}}
 => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
{{1,2},{3},{4},{5}}
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
{{1,3},{2},{4},{5}}
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
{{1},{2,3},{4},{5}}
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
{{1,4},{2},{3},{5}}
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
{{1},{2,4},{3},{5}}
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
{{1},{2},{3,4},{5}}
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
{{1,5},{2},{3},{4}}
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
{{1},{2,5},{3},{4}}
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
{{1},{2},{3,5},{4}}
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
{{1},{2},{3},{4,5}}
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
{{1},{2},{3},{4},{5}}
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 0
{{1,2,3},{4},{5},{6}}
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
{{1,2,4},{3},{5},{6}}
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
{{1,2},{3,4},{5,6}}
 => [2,2,2]
 => [2,2]
 => [2]
 => 3
{{1,2},{3,4},{5},{6}}
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
{{1,2,5},{3},{4},{6}}
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
{{1,2},{3,5},{4,6}}
 => [2,2,2]
 => [2,2]
 => [2]
 => 3
{{1,2},{3,5},{4},{6}}
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
{{1,2},{3,6},{4,5}}
 => [2,2,2]
 => [2,2]
 => [2]
 => 3
{{1,2},{3},{4,5},{6}}
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
{{1,2,6},{3},{4},{5}}
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
{{1,2},{3,6},{4},{5}}
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
{{1,2},{3},{4,6},{5}}
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
{{1,2},{3},{4},{5,6}}
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
{{1,2},{3},{4},{5},{6}}
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 0
{{1,3,4},{2},{5},{6}}
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
{{1,3},{2,4},{5,6}}
 => [2,2,2]
 => [2,2]
 => [2]
 => 3
{{1,3},{2,4},{5},{6}}
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
{{1,3,5},{2},{4},{6}}
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
{{1,3},{2,5},{4,6}}
 => [2,2,2]
 => [2,2]
 => [2]
 => 3
{{1,3},{2,5},{4},{6}}
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
{{1,3},{2,6},{4,5}}
 => [2,2,2]
 => [2,2]
 => [2]
 => 3
{{1,3},{2},{4,5},{6}}
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
{{1,3,6},{2},{4},{5}}
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
{{1,3},{2,6},{4},{5}}
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
{{1,3},{2},{4,6},{5}}
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
{{1,3},{2},{4},{5,6}}
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
{{1,3},{2},{4},{5},{6}}
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 0
{{1,4},{2,3},{5,6}}
 => [2,2,2]
 => [2,2]
 => [2]
 => 3
{{1,4},{2,3},{5},{6}}
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
{{1},{2,3,4},{5},{6}}
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
{{1,5},{2,3},{4,6}}
 => [2,2,2]
 => [2,2]
 => [2]
 => 3
{{1,5},{2,3},{4},{6}}
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
{{1},{2,3,5},{4},{6}}
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
{{1,6},{2,3},{4,5}}
 => [2,2,2]
 => [2,2]
 => [2]
 => 3
{{1},{2,3},{4,5},{6}}
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
{{1,6},{2,3},{4},{5}}
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
{{1},{2,3,6},{4},{5}}
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1
{{1},{2,3},{4,6},{5}}
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1
Description
The number of semistandard Young tableau of given shape, with entries at most 2. This is also the dimension of the corresponding irreducible representation of $GL_2$.
Matching statistic: St001232
Mapping
Mp00079: Set partitions —shape⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 25%
Values
{{1},{2},{3},{4}}
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1
{{1,2},{3},{4},{5}}
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 1
{{1,3},{2},{4},{5}}
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 1
{{1},{2,3},{4},{5}}
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 1
{{1,4},{2},{3},{5}}
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 1
{{1},{2,4},{3},{5}}
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 1
{{1},{2},{3,4},{5}}
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 1
{{1,5},{2},{3},{4}}
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 1
{{1},{2,5},{3},{4}}
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 1
{{1},{2},{3,5},{4}}
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 1
{{1},{2},{3},{4,5}}
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 1
{{1},{2},{3},{4},{5}}
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 0
{{1,2,3},{4},{5},{6}}
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 1
{{1,2,4},{3},{5},{6}}
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 1
{{1,2},{3,4},{5,6}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
{{1,2},{3,4},{5},{6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1,2,5},{3},{4},{6}}
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 1
{{1,2},{3,5},{4,6}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
{{1,2},{3,5},{4},{6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1,2},{3,6},{4,5}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
{{1,2},{3},{4,5},{6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1,2,6},{3},{4},{5}}
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 1
{{1,2},{3,6},{4},{5}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1,2},{3},{4,6},{5}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1,2},{3},{4},{5,6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1,2},{3},{4},{5},{6}}
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 0
{{1,3,4},{2},{5},{6}}
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 1
{{1,3},{2,4},{5,6}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
{{1,3},{2,4},{5},{6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1,3,5},{2},{4},{6}}
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 1
{{1,3},{2,5},{4,6}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
{{1,3},{2,5},{4},{6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1,3},{2,6},{4,5}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
{{1,3},{2},{4,5},{6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1,3,6},{2},{4},{5}}
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 1
{{1,3},{2,6},{4},{5}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1,3},{2},{4,6},{5}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1,3},{2},{4},{5,6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1,3},{2},{4},{5},{6}}
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 0
{{1,4},{2,3},{5,6}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
{{1,4},{2,3},{5},{6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1},{2,3,4},{5},{6}}
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 1
{{1,5},{2,3},{4,6}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
{{1,5},{2,3},{4},{6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1},{2,3,5},{4},{6}}
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 1
{{1,6},{2,3},{4,5}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
{{1},{2,3},{4,5},{6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1,6},{2,3},{4},{5}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1},{2,3,6},{4},{5}}
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 1
{{1},{2,3},{4,6},{5}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1},{2,3},{4},{5,6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1},{2,3},{4},{5},{6}}
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 0
{{1,4,5},{2},{3},{6}}
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 1
{{1,4},{2,5},{3,6}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
{{1,4},{2,5},{3},{6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1,4},{2,6},{3,5}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
{{1,4},{2},{3,5},{6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1,4,6},{2},{3},{5}}
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 1
{{1,4},{2,6},{3},{5}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1,4},{2},{3,6},{5}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1,4},{2},{3},{5,6}}
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1
{{1,5},{2,4},{3,6}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
{{1,6},{2,4},{3,5}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
{{1,5},{2,6},{3,4}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
{{1,6},{2,5},{3,4}}
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
{{1,2,3},{4,5},{6,7}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2,3},{4,6},{5,7}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2,3},{4,7},{5,6}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2,4},{3,5},{6,7}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2,4},{3,6},{5,7}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2,4},{3,7},{5,6}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2,5},{3,4},{6,7}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2},{3,4,5},{6,7}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2,6},{3,4},{5,7}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2},{3,4,6},{5,7}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2,7},{3,4},{5,6}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2},{3,4,7},{5,6}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2},{3,4},{5,6,7}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2,5},{3,6},{4,7}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2,5},{3,7},{4,6}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2,6},{3,5},{4,7}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2},{3,5,6},{4,7}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2,7},{3,5},{4,6}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2},{3,5,7},{4,6}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2},{3,5},{4,6,7}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2,6},{3,7},{4,5}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2,7},{3,6},{4,5}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2},{3,6,7},{4,5}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2},{3,6},{4,5,7}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2},{3,7},{4,5,6}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,3,4},{2,5},{6,7}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,3,4},{2,6},{5,7}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,3,4},{2,7},{5,6}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,3,5},{2,4},{6,7}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,3},{2,4,5},{6,7}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,3,6},{2,4},{5,7}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,3},{2,4,6},{5,7}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,3,7},{2,4},{5,6}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,3},{2,4,7},{5,6}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,3},{2,4},{5,6,7}}
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001645
Mapping
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 25%
Values
{{1},{2},{3},{4}}
 => [1,1,1,1] => [4] => ([],4)
 => ? = 1 + 6
{{1,2},{3},{4},{5}}
 => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ? = 1 + 6
{{1,3},{2},{4},{5}}
 => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ? = 1 + 6
{{1},{2,3},{4},{5}}
 => [1,2,1,1] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 6
{{1,4},{2},{3},{5}}
 => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ? = 1 + 6
{{1},{2,4},{3},{5}}
 => [1,2,1,1] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 6
{{1},{2},{3,4},{5}}
 => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
 => ? = 1 + 6
{{1,5},{2},{3},{4}}
 => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ? = 1 + 6
{{1},{2,5},{3},{4}}
 => [1,2,1,1] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 6
{{1},{2},{3,5},{4}}
 => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
 => ? = 1 + 6
{{1},{2},{3},{4,5}}
 => [1,1,1,2] => [1,4] => ([(3,4)],5)
 => ? = 1 + 6
{{1},{2},{3},{4},{5}}
 => [1,1,1,1,1] => [5] => ([],5)
 => ? = 0 + 6
{{1,2,3},{4},{5},{6}}
 => [3,1,1,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,2,4},{3},{5},{6}}
 => [3,1,1,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,2},{3,4},{5,6}}
 => [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 6
{{1,2},{3,4},{5},{6}}
 => [2,2,1,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,2,5},{3},{4},{6}}
 => [3,1,1,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,2},{3,5},{4,6}}
 => [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 6
{{1,2},{3,5},{4},{6}}
 => [2,2,1,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,2},{3,6},{4,5}}
 => [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 6
{{1,2},{3},{4,5},{6}}
 => [2,1,2,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,2,6},{3},{4},{5}}
 => [3,1,1,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,2},{3,6},{4},{5}}
 => [2,2,1,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,2},{3},{4,6},{5}}
 => [2,1,2,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,2},{3},{4},{5,6}}
 => [2,1,1,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,2},{3},{4},{5},{6}}
 => [2,1,1,1,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 0 + 6
{{1,3,4},{2},{5},{6}}
 => [3,1,1,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,3},{2,4},{5,6}}
 => [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 6
{{1,3},{2,4},{5},{6}}
 => [2,2,1,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,3,5},{2},{4},{6}}
 => [3,1,1,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,3},{2,5},{4,6}}
 => [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 6
{{1,3},{2,5},{4},{6}}
 => [2,2,1,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,3},{2,6},{4,5}}
 => [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 6
{{1,3},{2},{4,5},{6}}
 => [2,1,2,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,3,6},{2},{4},{5}}
 => [3,1,1,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,3},{2,6},{4},{5}}
 => [2,2,1,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,3},{2},{4,6},{5}}
 => [2,1,2,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,3},{2},{4},{5,6}}
 => [2,1,1,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,3},{2},{4},{5},{6}}
 => [2,1,1,1,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 0 + 6
{{1,4},{2,3},{5,6}}
 => [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 6
{{1,4},{2,3},{5},{6}}
 => [2,2,1,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1},{2,3,4},{5},{6}}
 => [1,3,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,5},{2,3},{4,6}}
 => [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 6
{{1,5},{2,3},{4},{6}}
 => [2,2,1,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1},{2,3,5},{4},{6}}
 => [1,3,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,6},{2,3},{4,5}}
 => [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 6
{{1},{2,3},{4,5},{6}}
 => [1,2,2,1] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,6},{2,3},{4},{5}}
 => [2,2,1,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1},{2,3,6},{4},{5}}
 => [1,3,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1},{2,3},{4,6},{5}}
 => [1,2,2,1] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 6
{{1,2,3,4},{5},{6},{7}}
 => [4,1,1,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
{{1,2,3,5},{4},{6},{7}}
 => [4,1,1,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
{{1,2,3,6},{4},{5},{7}}
 => [4,1,1,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
{{1,2,3,7},{4},{5},{6}}
 => [4,1,1,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
{{1,2,4,5},{3},{6},{7}}
 => [4,1,1,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
{{1,2,4,6},{3},{5},{7}}
 => [4,1,1,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
{{1,2,4,7},{3},{5},{6}}
 => [4,1,1,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
{{1,2,5,6},{3},{4},{7}}
 => [4,1,1,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
{{1,2,5,7},{3},{4},{6}}
 => [4,1,1,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
{{1,2,6,7},{3},{4},{5}}
 => [4,1,1,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
{{1,3,4,5},{2},{6},{7}}
 => [4,1,1,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
{{1,3,4,6},{2},{5},{7}}
 => [4,1,1,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
{{1,3,4,7},{2},{5},{6}}
 => [4,1,1,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
{{1,3,5,6},{2},{4},{7}}
 => [4,1,1,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
{{1,3,5,7},{2},{4},{6}}
 => [4,1,1,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
{{1,3,6,7},{2},{4},{5}}
 => [4,1,1,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
{{1,4,5,6},{2},{3},{7}}
 => [4,1,1,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
{{1,4,5,7},{2},{3},{6}}
 => [4,1,1,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
{{1,4,6,7},{2},{3},{5}}
 => [4,1,1,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
{{1,5,6,7},{2},{3},{4}}
 => [4,1,1,1] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 7 = 1 + 6
Description
The pebbling number of a connected graph.