Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001232
(load all 3 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => [1] => [1,0]
 => [1,0]
 => 0
{{1,2}}
 => [2,1] => [1,1,0,0]
 => [1,0,1,0]
 => 1
{{1},{2}}
 => [1,2] => [1,0,1,0]
 => [1,1,0,0]
 => 0
{{1,2,3}}
 => [2,3,1] => [1,1,0,1,0,0]
 => [1,1,0,0,1,0]
 => 1
{{1,2},{3}}
 => [2,1,3] => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 2
{{1},{2,3}}
 => [1,3,2] => [1,0,1,1,0,0]
 => [1,0,1,1,0,0]
 => 2
{{1},{2},{3}}
 => [1,2,3] => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0
{{1,2,3,4}}
 => [2,3,4,1] => [1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1
{{1,2,3},{4}}
 => [2,3,1,4] => [1,1,0,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => 2
{{1,2,4},{3}}
 => [2,4,3,1] => [1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => 3
{{1,2},{3},{4}}
 => [2,1,3,4] => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,0]
 => 3
{{1},{2,3,4}}
 => [1,3,4,2] => [1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => 4
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => 3
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 0
{{1,2,3,4,5}}
 => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1
{{1,2,3,4},{5}}
 => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
{{1,2,3,5},{4}}
 => [2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
{{1,2,3},{4},{5}}
 => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
{{1,2,4,5},{3}}
 => [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => 5
{{1,2,4},{3,5}}
 => [2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3
{{1,2,4},{3},{5}}
 => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 5
{{1,2},{3},{4},{5}}
 => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
{{1},{2,3,4,5}}
 => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 2
{{1},{2,3,4},{5}}
 => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => 4
{{1},{2,3,5},{4}}
 => [1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
{{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => 6
{{1},{2},{3,4,5}}
 => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
{{1},{2},{3,4},{5}}
 => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => 6
{{1},{2},{3},{4,5}}
 => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4
{{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 0
{{1,2,3,4,5,6}}
 => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1
{{1,2,3,4,5},{6}}
 => [2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
{{1,2,3,4,6},{5}}
 => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
{{1,2,3,4},{5},{6}}
 => [2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
{{1,2,3,5,6},{4}}
 => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,0,0,1,0]
 => 7
{{1,2,3,5},{4,6}}
 => [2,3,5,6,1,4] => [1,1,0,1,0,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => 4
{{1,2,3,5},{4},{6}}
 => [2,3,5,4,1,6] => [1,1,0,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => 6
{{1,2,3},{4},{5},{6}}
 => [2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
{{1,2,4,5,6},{3}}
 => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => 7
{{1,2,4,5},{3,6}}
 => [2,4,6,5,1,3] => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5
{{1,2,4,5},{3},{6}}
 => [2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => 8
{{1,2,4,6},{3,5}}
 => [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 3
{{1,2,4},{3,5,6}}
 => [2,4,5,1,6,3] => [1,1,0,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => 5
{{1,2,4},{3,5},{6}}
 => [2,4,5,1,3,6] => [1,1,0,1,1,0,1,0,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => 5
{{1,2,4},{3,6},{5}}
 => [2,4,6,1,5,3] => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5
{{1,2,4},{3},{5},{6}}
 => [2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => 7
{{1,2},{3},{4},{5},{6}}
 => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
{{1},{2,3,4,5,6}}
 => [1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2
{{1},{2,3,4,5},{6}}
 => [1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => 4
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.