Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000688
Mapping
Mp00252: Permutations —restriction⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
St000688: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1] => [1,0]
 => [1,0]
 => 0
[2,1] => [1] => [1,0]
 => [1,0]
 => 0
[1,2,3] => [1,2] => [1,0,1,0]
 => [1,1,0,0]
 => 0
[1,3,2] => [1,2] => [1,0,1,0]
 => [1,1,0,0]
 => 0
[2,1,3] => [2,1] => [1,1,0,0]
 => [1,0,1,0]
 => 0
[2,3,1] => [2,1] => [1,1,0,0]
 => [1,0,1,0]
 => 0
[3,1,2] => [1,2] => [1,0,1,0]
 => [1,1,0,0]
 => 0
[3,2,1] => [2,1] => [1,1,0,0]
 => [1,0,1,0]
 => 0
[1,2,3,4] => [1,2,3] => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0
[1,2,4,3] => [1,2,3] => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0
[1,3,2,4] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 1
[1,3,4,2] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 1
[1,4,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0
[1,4,3,2] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 1
[2,1,3,4] => [2,1,3] => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => 1
[2,1,4,3] => [2,1,3] => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => 1
[2,3,1,4] => [2,3,1] => [1,1,0,1,0,0]
 => [1,1,0,1,0,0]
 => 1
[2,3,4,1] => [2,3,1] => [1,1,0,1,0,0]
 => [1,1,0,1,0,0]
 => 1
[2,4,1,3] => [2,1,3] => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => 1
[2,4,3,1] => [2,3,1] => [1,1,0,1,0,0]
 => [1,1,0,1,0,0]
 => 1
[3,1,2,4] => [3,1,2] => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => 0
[3,1,4,2] => [3,1,2] => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => 0
[3,2,1,4] => [3,2,1] => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => 0
[3,2,4,1] => [3,2,1] => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => 0
[3,4,1,2] => [3,1,2] => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => 0
[3,4,2,1] => [3,2,1] => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => 0
[4,1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0
[4,1,3,2] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 1
[4,2,1,3] => [2,1,3] => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => 1
[4,2,3,1] => [2,3,1] => [1,1,0,1,0,0]
 => [1,1,0,1,0,0]
 => 1
[4,3,1,2] => [3,1,2] => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => 0
[4,3,2,1] => [3,2,1] => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => 0
[1,2,3,4,5] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 0
[1,2,3,5,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 0
[1,2,4,3,5] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[1,2,4,5,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[1,2,5,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 0
[1,2,5,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[1,3,2,4,5] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => 1
[1,3,2,5,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => 1
[1,3,4,2,5] => [1,3,4,2] => [1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0]
 => 1
[1,3,4,5,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0]
 => 1
[1,3,5,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => 1
[1,3,5,4,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,0,0]
 => 1
[1,4,2,3,5] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => 2
[1,4,2,5,3] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => 2
[1,4,3,2,5] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => 2
[1,4,3,5,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => 2
[1,4,5,2,3] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => 2
[1,4,5,3,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => 2
Description
The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. The global dimension is given by [[St000684]] and the dominant dimension is given by [[St000685]]. To every Dyck path there is an LNakayama algebra associated as described in [[St000684]]. Dyck paths for which the global dimension and the dominant dimension of the the LNakayama algebra coincide and both dimensions at least $2$ correspond to the LNakayama algebras that are higher Auslander algebras in the sense of [1].