Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001431
Mapping
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00122: Dyck paths —Elizalde-Deutsch bijection⟶ Dyck paths
St001431: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1,1]
 => [1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => 0
[2,2]
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 1
[2,1,1]
 => [1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => 0
[1,1,1,1]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => 1
[3,2]
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 1
[3,1,1]
 => [1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => 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]
 => 1
[1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0]
 => 1
[4,2]
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 1
[4,1,1]
 => [1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => 0
[3,3]
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,0,0,1,0]
 => 1
[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]
 => 1
[2,2,2]
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => 0
[2,2,1,1]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 2
[2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0]
 => 1
[1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 1
[5,2]
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 1
[5,1,1]
 => [1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => 0
[4,3]
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,0,0,1,0]
 => 1
[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]
 => 1
[3,3,1]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => 2
[3,2,2]
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => 0
[3,2,1,1]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 2
[3,1,1,1,1]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0]
 => 1
[2,2,2,1]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => 1
[2,2,1,1,1]
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => 2
[2,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 1
[6,2]
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 1
[6,1,1]
 => [1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => 0
[5,3]
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,0,0,1,0]
 => 1
[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]
 => 1
[4,4]
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => 1
[4,3,1]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => 2
[4,2,2]
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => 0
[4,2,1,1]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 2
[4,1,1,1,1]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0]
 => 1
[3,3,2]
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => 3
[3,3,1,1]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => 2
[3,2,2,1]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => 1
[3,2,1,1,1]
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => 2
[3,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 1
[2,2,2,2]
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => 0
[2,2,2,1,1]
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 2
[7,2]
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 1
[7,1,1]
 => [1,1]
 => [1,1,0,0]
 => [1,0,1,0]
 => 0
[6,3]
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,0,0,1,0]
 => 1
Description
Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. The modified algebra B is obtained from the stable Auslander algebra kQ/I by deleting all relations which contain walks of length at least three (conjectural this step of deletion is not necessary as the stable higher Auslander algebras might be quadratic) and taking as B then the algebra kQ^(op)/J when J is the quadratic perp of the ideal I. See http://www.findstat.org/DyckPaths/NakayamaAlgebras for the definition of Loewy length and Nakayama algebras associated to Dyck paths.