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Your data matches 44 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001498
Mapping
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
St001498: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => 2
[1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 3
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 3
[1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 3
[1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 2
[1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 2
[1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 3
[1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => 2
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0,1,1,0,0]
 => 3
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0,1,1,0,0]
 => 3
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0,1,1,0,0]
 => 3
[1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 2
[1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 2
[1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 2
[1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 2
[1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 2
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 2
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => 2
[1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => 2
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0,1,1,0,0]
 => 3
[1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,1,1,0,0,0]
 => 2
[1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,1,1,0,0,0]
 => 2
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,1,1,0,0,0]
 => 2
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => 2
Description
The normalised height of a Nakayama algebra with magnitude 1. We use the bijection (see code) suggested by Christian Stump, to have a bijection between such Nakayama algebras with magnitude 1 and Dyck paths. The normalised height is the height of the (periodic) Dyck path given by the top of the Auslander-Reiten quiver. Thus when having a CNakayama algebra it is the Loewy length minus the number of simple modules and for the LNakayama algebras it is the usual height.
Matching statistic: St000617
Mapping
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
Mp00132: Dyck paths —switch returns and last double rise⟶ Dyck paths
St000617: Dyck paths ⟶ ℤResult quality: 88% ●values known / values provided: 88%●distinct values known / distinct values provided: 100%
Values
[1,1,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => 2
[1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => 3
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => 3
[1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => 3
[1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 2
[1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 2
[1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 2
[1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => 3
[1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 2
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 4
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 4
[1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 4
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 3
[1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 3
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 3
[1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 4
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => 3
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 4
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 4
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 4
[1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 3
[1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 3
[1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 3
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 4
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => 3
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 4
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 4
[1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 3
[1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 3
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 3
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 4
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => 3
[1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => 2
[1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => 2
[1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => 2
[1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => 2
[1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => 2
[1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => 2
[1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => 2
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => 2
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => 2
[1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 3
[1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 3
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 3
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => 2
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => 3
[1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0]
 => 2
[1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0]
 => 2
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0]
 => 2
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
 => ? = 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
 => ? = 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
 => ? = 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
 => ? = 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
 => ? = 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
 => ? = 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
 => ? = 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0,1,0]
 => ? = 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0,1,0]
 => ? = 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0,1,0]
 => ? = 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0,1,0]
 => ? = 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0,1,0]
 => ? = 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0,1,0]
 => ? = 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
 => ? = 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0,1,0]
 => ? = 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0,1,0]
 => ? = 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0,1,0]
 => ? = 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
 => ? = 3
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
 => [1,0,1,1,0,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
 => ? = 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0,1,0]
 => ? = 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0,1,0]
 => ? = 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0,1,0]
 => ? = 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0,1,0]
 => ? = 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => [1,0,1,1,1,0,0,1,0,1,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0,1,0]
 => ? = 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
 => [1,0,1,1,1,0,1,0,0,1,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0,1,0]
 => ? = 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
 => ? = 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
 => ? = 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
 => ? = 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0,1,0]
 => ? = 2
Description
The number of global maxima of a Dyck path.
Matching statistic: St001232
(load all 3 compositions to match this statistic)
Mapping
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 62% ●values known / values provided: 62%●distinct values known / distinct values provided: 100%
Values
[1,1,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => 2
[1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => ? = 2
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => ? = 3
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => ? = 3
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => ? = 3
[1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => ? = 2
[1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => ? = 2
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => ? = 3
[1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => ? = 2
[1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => ? = 2
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => ? = 2
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => ? = 2
[1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => ? = 3
[1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => ? = 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 5
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 5
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 5
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 5
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,1,0,0,0]
 => ? = 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
 => ? = 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
 => ? = 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => ? = 3
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => ? = 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => ? = 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
 => ? = 3
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,1,0,0,0]
 => ? = 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
 => ? = 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
 => ? = 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => ? = 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => ? = 3
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => ? = 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
 => ? = 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,1,0,0,0]
 => ? = 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,1,0,0]
 => ? = 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,1,0,0]
 => ? = 3
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St000120
(load all 2 compositions to match this statistic)
Mapping
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St000120: Dyck paths ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 75%
Values
[1,1,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => 2
[1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 3
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 3
[1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 3
[1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 2
[1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 2
[1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 3
[1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => 2
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => 3
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => 3
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 4
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => 3
[1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 2
[1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 2
[1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 2
[1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 2
[1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 2
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 2
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => 2
[1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => 2
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => 3
[1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => 2
[1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => 2
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => 2
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 5
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => ? = 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 5
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 5
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 5
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 5
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => ? = 4
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 5
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 5
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 5
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => ? = 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
 => ? = 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
 => ? = 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => ? = 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => ? = 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,1,0,0,0]
 => ? = 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 5
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 5
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 5
Description
The number of left tunnels of a Dyck path. A tunnel is a pair (a,b) where a is the position of an open parenthesis and b is the position of the matching close parenthesis. If a+b
Matching statistic: St000335
(load all 2 compositions to match this statistic)
Mapping
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
Mp00032: Dyck paths —inverse zeta map⟶ Dyck paths
St000335: Dyck paths ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 75%
Values
[1,1,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,0]
 => 2
[1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => 2
[1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => 2
[1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 2
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => 4
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => 4
[1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => 4
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 3
[1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 3
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 3
[1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => 4
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => 4
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => 4
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => 4
[1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 3
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => 4
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => 4
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => 4
[1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 3
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => 4
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 2
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => 2
[1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 3
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => 2
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => 2
[1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => 2
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => 2
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 5
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => ? = 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => ? = 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => ? = 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,1,0,0,0,0,0]
 => ? = 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 5
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 5
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 5
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => ? = 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => ? = 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => ? = 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 5
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,1,0,0,0,0,0]
 => ? = 4
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 5
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 5
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => ? = 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => ? = 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => ? = 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 5
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,1,0,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,1,1,1,0,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,1,1,1,0,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,1,0,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,1,1,0,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,1,1,0,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,1,1,0,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,1,1,1,0,0,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,1,0,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,0,1,0,1,1,1,0,0,0,0]
 => ? = 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 5
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 5
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => ? = 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => ? = 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => ? = 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 5
Description
The difference of lower and upper interactions. An ''upper interaction'' in a Dyck path is the occurrence of a factor $0^k 1^k$ with $k \geq 1$ (see [[St000331]]), and a ''lower interaction'' is the occurrence of a factor $1^k 0^k$ with $k \geq 1$. In both cases, $1$ denotes an up-step $0$ denotes a a down-step.
Matching statistic: St001184
Mapping
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
St001184: Dyck paths ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 75%
Values
[1,1,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => 2
[1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => 2
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 3
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 3
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 3
[1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => 2
[1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => 2
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 3
[1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => 2
[1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => 2
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => 2
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,1,0,0,0]
 => ? = 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
Description
Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra.
Matching statistic: St001185
Mapping
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
St001185: Dyck paths ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 75%
Values
[1,1,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => 2
[1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => 2
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 3
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 3
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 3
[1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => 2
[1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => 2
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 3
[1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => 2
[1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => 2
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => 2
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,1,0,0,0]
 => ? = 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
Description
The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra.
Matching statistic: St001194
Mapping
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
Mp00028: Dyck paths —reverse⟶ Dyck paths
St001194: Dyck paths ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 75%
Values
[1,1,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2
[1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 2
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => 3
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => 3
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => 3
[1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => 3
[1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => 2
[1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => 2
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => 2
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
 => ? = 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
Description
The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module
Matching statistic: St001201
Mapping
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
Mp00028: Dyck paths —reverse⟶ Dyck paths
St001201: Dyck paths ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 75%
Values
[1,1,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 2
[1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 2
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => 3
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => 3
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 4
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => 3
[1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 3
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 2
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => 3
[1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => 2
[1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => 2
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => 2
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
 => ? = 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5
Description
The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path.
Matching statistic: St001481
Mapping
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
St001481: Dyck paths ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 75%
Values
[1,1,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => 2
[1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => 2
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 3
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 3
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 3
[1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => 2
[1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => 2
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 3
[1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => 2
[1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => 2
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => 2
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
 => ? = 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => ? = 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,1,0,0,0]
 => ? = 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => ? = 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 5
Description
The minimal height of a peak of a Dyck path.
The following 34 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000338The number of pixed points of a permutation. St001008Number of indecomposable injective modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular module. St001226The number of integers i such that the radical of the i-th indecomposable projective module has vanishing first extension group with the Jacobson radical J in the corresponding Nakayama algebra. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra. St001265The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra. St001113Number of indecomposable projective non-injective modules with reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001292The injective dimension of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001473The absolute value of the sum of all entries of the Coxeter matrix of the corresponding LNakayama algebra. St001872The number of indecomposable injective modules with even projective dimension in the corresponding Nakayama algebra. St000731The number of double exceedences of a permutation. St000054The first entry of the permutation. St000007The number of saliances of the permutation. St000352The Elizalde-Pak rank of a permutation. St000542The number of left-to-right-minima of a permutation. St000990The first ascent of a permutation. St001737The number of descents of type 2 in a permutation. St000153The number of adjacent cycles of a permutation. St000215The number of adjacencies of a permutation, zero appended. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000546The number of global descents of a permutation. St000845The maximal number of elements covered by an element in a poset. St000022The number of fixed points of a permutation. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St000864The number of circled entries of the shifted recording tableau of a permutation. St000439The position of the first down step of a Dyck path. St000124The cardinality of the preimage of the Simion-Schmidt map. St000660The number of rises of length at least 3 of a Dyck path. St000647The number of big descents of a permutation. St000850The number of 1/2-balanced pairs in a poset. St001085The number of occurrences of the vincular pattern |21-3 in a permutation.