Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001232
Mapping
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1]
 => [1]
 => [1,0]
 => [1,0]
 => 0
[2,1]
 => [1]
 => [1,0]
 => [1,0]
 => 0
[1,1,1]
 => [1,1]
 => [1,1,0,0]
 => [1,1,0,0]
 => 0
[3,1]
 => [1]
 => [1,0]
 => [1,0]
 => 0
[2,2]
 => [2]
 => [1,0,1,0]
 => [1,0,1,0]
 => 1
[2,1,1]
 => [1,1]
 => [1,1,0,0]
 => [1,1,0,0]
 => 0
[1,1,1,1]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => 2
[4,1]
 => [1]
 => [1,0]
 => [1,0]
 => 0
[3,2]
 => [2]
 => [1,0,1,0]
 => [1,0,1,0]
 => 1
[3,1,1]
 => [1,1]
 => [1,1,0,0]
 => [1,1,0,0]
 => 0
[2,2,1]
 => [2,1]
 => [1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => 2
[2,1,1,1]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => 2
[5,1]
 => [1]
 => [1,0]
 => [1,0]
 => 0
[4,2]
 => [2]
 => [1,0,1,0]
 => [1,0,1,0]
 => 1
[4,1,1]
 => [1,1]
 => [1,1,0,0]
 => [1,1,0,0]
 => 0
[3,2,1]
 => [2,1]
 => [1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => 2
[3,1,1,1]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => 2
[2,2,2]
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => 0
[6,1]
 => [1]
 => [1,0]
 => [1,0]
 => 0
[5,2]
 => [2]
 => [1,0,1,0]
 => [1,0,1,0]
 => 1
[5,1,1]
 => [1,1]
 => [1,1,0,0]
 => [1,1,0,0]
 => 0
[4,2,1]
 => [2,1]
 => [1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => 2
[4,1,1,1]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => 2
[3,2,2]
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => 0
[2,2,2,1]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[7,1]
 => [1]
 => [1,0]
 => [1,0]
 => 0
[6,2]
 => [2]
 => [1,0,1,0]
 => [1,0,1,0]
 => 1
[6,1,1]
 => [1,1]
 => [1,1,0,0]
 => [1,1,0,0]
 => 0
[5,2,1]
 => [2,1]
 => [1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => 2
[5,1,1,1]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => 2
[4,2,2]
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => 0
[3,3,2]
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
[3,2,2,1]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[2,2,2,2]
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => 0
[8,1]
 => [1]
 => [1,0]
 => [1,0]
 => 0
[7,2]
 => [2]
 => [1,0,1,0]
 => [1,0,1,0]
 => 1
[7,1,1]
 => [1,1]
 => [1,1,0,0]
 => [1,1,0,0]
 => 0
[6,2,1]
 => [2,1]
 => [1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => 2
[6,1,1,1]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => 2
[5,2,2]
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => 0
[4,3,2]
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
[4,2,2,1]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[3,3,3]
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => 3
[3,2,2,2]
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => 0
[2,2,2,2,1]
 => [2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[9,1]
 => [1]
 => [1,0]
 => [1,0]
 => 0
[8,2]
 => [2]
 => [1,0,1,0]
 => [1,0,1,0]
 => 1
[8,1,1]
 => [1,1]
 => [1,1,0,0]
 => [1,1,0,0]
 => 0
[7,2,1]
 => [2,1]
 => [1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => 2
[7,1,1,1]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => 2
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.