Your data matches 5 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000421
Mapping
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St000421: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => [1,1,0,0]
 => [2] => [1,1,0,0]
 => 1
[1,0,1,0]
 => [1,1,0,1,0,0]
 => [2,1] => [1,1,0,0,1,0]
 => 1
[1,1,0,0]
 => [1,1,1,0,0,0]
 => [3] => [1,1,1,0,0,0]
 => 4
[1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => 1
[1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [2,2] => [1,1,0,0,1,1,0,0]
 => 3
[1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [3,1] => [1,1,1,0,0,0,1,0]
 => 4
[1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => [3,1] => [1,1,1,0,0,0,1,0]
 => 4
[1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [4] => [1,1,1,1,0,0,0,0]
 => 13
[1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => 1
[1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => 3
[1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => 3
[1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => 3
[1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => 9
[1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => 4
[1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => 9
[1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => 4
[1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => 4
[1,1,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => 9
[1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => 13
[1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => 13
[1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => 13
[1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [5] => [1,1,1,1,1,0,0,0,0,0]
 => 41
[1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]
 => 1
[1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0]
 => 3
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
 => 3
[1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,0,0]
 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
 => 3
[1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
 => 9
[1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0]
 => 3
[1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]
 => 7
[1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,0]
 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0]
 => 3
[1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0]
 => 3
[1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]
 => 7
[1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0]
 => 9
[1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0]
 => 9
[1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0]
 => 9
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 27
[1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 4
[1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
 => 9
[1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 9
[1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,1,0,1,0,0,0]
 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 9
[1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 24
[1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 4
[1,1,0,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,1,0,0,0]
 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
 => 9
[1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 4
[1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 4
[1,1,0,1,0,1,1,0,0,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
 => 9
[1,1,0,1,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 9
[1,1,0,1,1,0,0,1,0,0]
 => [1,1,1,0,1,1,0,0,1,0,0,0]
 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 9
[1,1,0,1,1,0,1,0,0,0]
 => [1,1,1,0,1,1,0,1,0,0,0,0]
 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 9
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 24
Description
The number of Dyck paths that are weakly below a Dyck path, except for the path itself.
Matching statistic: St000418
Mapping
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St000418: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => [1,1,0,0]
 => [2] => [1,1,0,0]
 => 2 = 1 + 1
[1,0,1,0]
 => [1,1,0,1,0,0]
 => [2,1] => [1,1,0,0,1,0]
 => 2 = 1 + 1
[1,1,0,0]
 => [1,1,1,0,0,0]
 => [3] => [1,1,1,0,0,0]
 => 5 = 4 + 1
[1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => 2 = 1 + 1
[1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [2,2] => [1,1,0,0,1,1,0,0]
 => 4 = 3 + 1
[1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [3,1] => [1,1,1,0,0,0,1,0]
 => 5 = 4 + 1
[1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => [3,1] => [1,1,1,0,0,0,1,0]
 => 5 = 4 + 1
[1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [4] => [1,1,1,1,0,0,0,0]
 => 14 = 13 + 1
[1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => 2 = 1 + 1
[1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => 4 = 3 + 1
[1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => 4 = 3 + 1
[1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => 4 = 3 + 1
[1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => 10 = 9 + 1
[1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => 5 = 4 + 1
[1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => 10 = 9 + 1
[1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => 5 = 4 + 1
[1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => 5 = 4 + 1
[1,1,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => 10 = 9 + 1
[1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => 14 = 13 + 1
[1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => 14 = 13 + 1
[1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => 14 = 13 + 1
[1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [5] => [1,1,1,1,1,0,0,0,0,0]
 => 42 = 41 + 1
[1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]
 => 2 = 1 + 1
[1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0]
 => 4 = 3 + 1
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
 => 4 = 3 + 1
[1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,0,0]
 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
 => 4 = 3 + 1
[1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
 => 10 = 9 + 1
[1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0]
 => 4 = 3 + 1
[1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]
 => 8 = 7 + 1
[1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,0]
 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0]
 => 4 = 3 + 1
[1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0]
 => 4 = 3 + 1
[1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]
 => 8 = 7 + 1
[1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0]
 => 10 = 9 + 1
[1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0]
 => 10 = 9 + 1
[1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0]
 => 10 = 9 + 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 28 = 27 + 1
[1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 5 = 4 + 1
[1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
 => 10 = 9 + 1
[1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 10 = 9 + 1
[1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,1,0,1,0,0,0]
 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 10 = 9 + 1
[1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 25 = 24 + 1
[1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 5 = 4 + 1
[1,1,0,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,1,0,0,0]
 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
 => 10 = 9 + 1
[1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 5 = 4 + 1
[1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 5 = 4 + 1
[1,1,0,1,0,1,1,0,0,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
 => 10 = 9 + 1
[1,1,0,1,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 10 = 9 + 1
[1,1,0,1,1,0,0,1,0,0]
 => [1,1,1,0,1,1,0,0,1,0,0,0]
 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 10 = 9 + 1
[1,1,0,1,1,0,1,0,0,0]
 => [1,1,1,0,1,1,0,1,0,0,0,0]
 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 10 = 9 + 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 25 = 24 + 1
Description
The number of Dyck paths that are weakly below a Dyck path.
Matching statistic: St000032
Mapping
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St000032: Dyck paths ⟶ ℤResult quality: 60% ●values known / values provided: 60%●distinct values known / distinct values provided: 78%
Values
[1,0]
 => [1,1,0,0]
 => [2] => [1,1,0,0]
 => 2 = 1 + 1
[1,0,1,0]
 => [1,1,0,1,0,0]
 => [2,1] => [1,1,0,0,1,0]
 => 2 = 1 + 1
[1,1,0,0]
 => [1,1,1,0,0,0]
 => [3] => [1,1,1,0,0,0]
 => 5 = 4 + 1
[1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => 2 = 1 + 1
[1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [2,2] => [1,1,0,0,1,1,0,0]
 => 4 = 3 + 1
[1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [3,1] => [1,1,1,0,0,0,1,0]
 => 5 = 4 + 1
[1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => [3,1] => [1,1,1,0,0,0,1,0]
 => 5 = 4 + 1
[1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [4] => [1,1,1,1,0,0,0,0]
 => 14 = 13 + 1
[1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => 2 = 1 + 1
[1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => 4 = 3 + 1
[1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => 4 = 3 + 1
[1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => 4 = 3 + 1
[1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => 10 = 9 + 1
[1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => 5 = 4 + 1
[1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => 10 = 9 + 1
[1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => 5 = 4 + 1
[1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => 5 = 4 + 1
[1,1,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => 10 = 9 + 1
[1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => 14 = 13 + 1
[1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => 14 = 13 + 1
[1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => 14 = 13 + 1
[1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [5] => [1,1,1,1,1,0,0,0,0,0]
 => 42 = 41 + 1
[1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]
 => 2 = 1 + 1
[1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0]
 => 4 = 3 + 1
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
 => 4 = 3 + 1
[1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,0,0]
 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
 => 4 = 3 + 1
[1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
 => 10 = 9 + 1
[1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0]
 => 4 = 3 + 1
[1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]
 => 8 = 7 + 1
[1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,0]
 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0]
 => 4 = 3 + 1
[1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0]
 => 4 = 3 + 1
[1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]
 => 8 = 7 + 1
[1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0]
 => 10 = 9 + 1
[1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0]
 => 10 = 9 + 1
[1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0]
 => 10 = 9 + 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 28 = 27 + 1
[1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 5 = 4 + 1
[1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
 => 10 = 9 + 1
[1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 10 = 9 + 1
[1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,1,0,1,0,0,0]
 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 10 = 9 + 1
[1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 25 = 24 + 1
[1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 5 = 4 + 1
[1,1,0,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,1,0,0,0]
 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
 => 10 = 9 + 1
[1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 5 = 4 + 1
[1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 5 = 4 + 1
[1,1,0,1,0,1,1,0,0,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
 => 10 = 9 + 1
[1,1,0,1,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 10 = 9 + 1
[1,1,0,1,1,0,0,1,0,0]
 => [1,1,1,0,1,1,0,0,1,0,0,0]
 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 10 = 9 + 1
[1,1,0,1,1,0,1,0,0,0]
 => [1,1,1,0,1,1,0,1,0,0,0,0]
 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 10 = 9 + 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 25 = 24 + 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
 => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 3 + 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
 => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 3 + 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
 => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 3 + 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
 => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => ? = 9 + 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
 => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3 + 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
 => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => ? = 7 + 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]
 => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3 + 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3 + 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
 => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => ? = 7 + 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
 => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => ? = 9 + 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
 => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => ? = 9 + 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
 => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => ? = 9 + 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
 => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => ? = 27 + 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
 => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 3 + 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => ? = 7 + 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => ? = 7 + 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]
 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => ? = 7 + 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
 => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 19 + 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]
 => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 3 + 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]
 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => ? = 7 + 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]
 => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 3 + 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 3 + 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => ? = 7 + 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]
 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => ? = 7 + 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => ? = 7 + 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
 => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => ? = 7 + 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
 => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 19 + 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
 => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 9 + 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
 => ? = 19 + 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
 => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 9 + 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
 => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 9 + 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
 => ? = 19 + 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
 => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 9 + 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
 => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]
 => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 9 + 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
 => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 9 + 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
 => ? = 19 + 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
 => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 27 + 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
 => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 27 + 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
 => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 27 + 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
 => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 27 + 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => ? = 83 + 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 3 + 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
 => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => ? = 7 + 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]
 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => ? = 7 + 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => ? = 7 + 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
 => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
 => ? = 19 + 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]
 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => ? = 7 + 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 15 + 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]
 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => ? = 7 + 1
Description
The number of elements smaller than the given Dyck path in the Tamari Order.
Matching statistic: St000950
(load all 19 compositions to match this statistic)
Mapping
St000950: Dyck paths ⟶ ℤResult quality: 20% ●values known / values provided: 20%●distinct values known / distinct values provided: 56%
Values
[1,0]
 => 2 = 1 + 1
[1,0,1,0]
 => 2 = 1 + 1
[1,1,0,0]
 => 5 = 4 + 1
[1,0,1,0,1,0]
 => 2 = 1 + 1
[1,0,1,1,0,0]
 => 4 = 3 + 1
[1,1,0,0,1,0]
 => 5 = 4 + 1
[1,1,0,1,0,0]
 => 5 = 4 + 1
[1,1,1,0,0,0]
 => 14 = 13 + 1
[1,0,1,0,1,0,1,0]
 => 2 = 1 + 1
[1,0,1,0,1,1,0,0]
 => 4 = 3 + 1
[1,0,1,1,0,0,1,0]
 => 4 = 3 + 1
[1,0,1,1,0,1,0,0]
 => 4 = 3 + 1
[1,0,1,1,1,0,0,0]
 => 10 = 9 + 1
[1,1,0,0,1,0,1,0]
 => 5 = 4 + 1
[1,1,0,0,1,1,0,0]
 => 10 = 9 + 1
[1,1,0,1,0,0,1,0]
 => 5 = 4 + 1
[1,1,0,1,0,1,0,0]
 => 5 = 4 + 1
[1,1,0,1,1,0,0,0]
 => 10 = 9 + 1
[1,1,1,0,0,0,1,0]
 => 14 = 13 + 1
[1,1,1,0,0,1,0,0]
 => 14 = 13 + 1
[1,1,1,0,1,0,0,0]
 => 14 = 13 + 1
[1,1,1,1,0,0,0,0]
 => 42 = 41 + 1
[1,0,1,0,1,0,1,0,1,0]
 => 2 = 1 + 1
[1,0,1,0,1,0,1,1,0,0]
 => 4 = 3 + 1
[1,0,1,0,1,1,0,0,1,0]
 => 4 = 3 + 1
[1,0,1,0,1,1,0,1,0,0]
 => 4 = 3 + 1
[1,0,1,0,1,1,1,0,0,0]
 => 10 = 9 + 1
[1,0,1,1,0,0,1,0,1,0]
 => 4 = 3 + 1
[1,0,1,1,0,0,1,1,0,0]
 => 8 = 7 + 1
[1,0,1,1,0,1,0,0,1,0]
 => 4 = 3 + 1
[1,0,1,1,0,1,0,1,0,0]
 => 4 = 3 + 1
[1,0,1,1,0,1,1,0,0,0]
 => 8 = 7 + 1
[1,0,1,1,1,0,0,0,1,0]
 => 10 = 9 + 1
[1,0,1,1,1,0,0,1,0,0]
 => 10 = 9 + 1
[1,0,1,1,1,0,1,0,0,0]
 => 10 = 9 + 1
[1,0,1,1,1,1,0,0,0,0]
 => 28 = 27 + 1
[1,1,0,0,1,0,1,0,1,0]
 => 5 = 4 + 1
[1,1,0,0,1,0,1,1,0,0]
 => 10 = 9 + 1
[1,1,0,0,1,1,0,0,1,0]
 => 10 = 9 + 1
[1,1,0,0,1,1,0,1,0,0]
 => 10 = 9 + 1
[1,1,0,0,1,1,1,0,0,0]
 => 25 = 24 + 1
[1,1,0,1,0,0,1,0,1,0]
 => 5 = 4 + 1
[1,1,0,1,0,0,1,1,0,0]
 => 10 = 9 + 1
[1,1,0,1,0,1,0,0,1,0]
 => 5 = 4 + 1
[1,1,0,1,0,1,0,1,0,0]
 => 5 = 4 + 1
[1,1,0,1,0,1,1,0,0,0]
 => 10 = 9 + 1
[1,1,0,1,1,0,0,0,1,0]
 => 10 = 9 + 1
[1,1,0,1,1,0,0,1,0,0]
 => 10 = 9 + 1
[1,1,0,1,1,0,1,0,0,0]
 => 10 = 9 + 1
[1,1,0,1,1,1,0,0,0,0]
 => 25 = 24 + 1
[1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
[1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 3 + 1
[1,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 3 + 1
[1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 3 + 1
[1,0,1,0,1,0,1,1,1,0,0,0]
 => ? = 9 + 1
[1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3 + 1
[1,0,1,0,1,1,0,0,1,1,0,0]
 => ? = 7 + 1
[1,0,1,0,1,1,0,1,0,0,1,0]
 => ? = 3 + 1
[1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 3 + 1
[1,0,1,0,1,1,0,1,1,0,0,0]
 => ? = 7 + 1
[1,0,1,0,1,1,1,0,0,0,1,0]
 => ? = 9 + 1
[1,0,1,0,1,1,1,0,0,1,0,0]
 => ? = 9 + 1
[1,0,1,0,1,1,1,0,1,0,0,0]
 => ? = 9 + 1
[1,0,1,0,1,1,1,1,0,0,0,0]
 => ? = 27 + 1
[1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 3 + 1
[1,0,1,1,0,0,1,0,1,1,0,0]
 => ? = 7 + 1
[1,0,1,1,0,0,1,1,0,0,1,0]
 => ? = 7 + 1
[1,0,1,1,0,0,1,1,0,1,0,0]
 => ? = 7 + 1
[1,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 19 + 1
[1,0,1,1,0,1,0,0,1,0,1,0]
 => ? = 3 + 1
[1,0,1,1,0,1,0,0,1,1,0,0]
 => ? = 7 + 1
[1,0,1,1,0,1,0,1,0,0,1,0]
 => ? = 3 + 1
[1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 3 + 1
[1,0,1,1,0,1,0,1,1,0,0,0]
 => ? = 7 + 1
[1,0,1,1,0,1,1,0,0,0,1,0]
 => ? = 7 + 1
[1,0,1,1,0,1,1,0,0,1,0,0]
 => ? = 7 + 1
[1,0,1,1,0,1,1,0,1,0,0,0]
 => ? = 7 + 1
[1,0,1,1,0,1,1,1,0,0,0,0]
 => ? = 19 + 1
[1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 9 + 1
[1,0,1,1,1,0,0,0,1,1,0,0]
 => ? = 19 + 1
[1,0,1,1,1,0,0,1,0,0,1,0]
 => ? = 9 + 1
[1,0,1,1,1,0,0,1,0,1,0,0]
 => ? = 9 + 1
[1,0,1,1,1,0,0,1,1,0,0,0]
 => ? = 19 + 1
[1,0,1,1,1,0,1,0,0,0,1,0]
 => ? = 9 + 1
[1,0,1,1,1,0,1,0,0,1,0,0]
 => ? = 9 + 1
[1,0,1,1,1,0,1,0,1,0,0,0]
 => ? = 9 + 1
[1,0,1,1,1,0,1,1,0,0,0,0]
 => ? = 19 + 1
[1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 27 + 1
[1,0,1,1,1,1,0,0,0,1,0,0]
 => ? = 27 + 1
[1,0,1,1,1,1,0,0,1,0,0,0]
 => ? = 27 + 1
[1,0,1,1,1,1,0,1,0,0,0,0]
 => ? = 27 + 1
[1,0,1,1,1,1,1,0,0,0,0,0]
 => ? = 83 + 1
[1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 4 + 1
[1,1,0,0,1,0,1,0,1,1,0,0]
 => ? = 9 + 1
[1,1,0,0,1,0,1,1,0,0,1,0]
 => ? = 9 + 1
[1,1,0,0,1,0,1,1,0,1,0,0]
 => ? = 9 + 1
[1,1,0,0,1,0,1,1,1,0,0,0]
 => ? = 24 + 1
[1,1,0,0,1,1,0,0,1,0,1,0]
 => ? = 9 + 1
[1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 19 + 1
[1,1,0,0,1,1,0,1,0,0,1,0]
 => ? = 9 + 1
Description
Number of tilting modules of the corresponding LNakayama algebra, where a tilting module is a generalised tilting module of projective dimension 1.
Matching statistic: St000082
Mapping
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
St000082: Binary trees ⟶ ℤResult quality: 20% ●values known / values provided: 20%●distinct values known / distinct values provided: 56%
Values
[1,0]
 => [1,1,0,0]
 => [1,2] => [.,[.,.]]
 => 2 = 1 + 1
[1,0,1,0]
 => [1,1,0,1,0,0]
 => [2,1,3] => [[.,.],[.,.]]
 => 2 = 1 + 1
[1,1,0,0]
 => [1,1,1,0,0,0]
 => [1,2,3] => [.,[.,[.,.]]]
 => 5 = 4 + 1
[1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [3,2,1,4] => [[[.,.],.],[.,.]]
 => 2 = 1 + 1
[1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [2,3,1,4] => [[.,[.,.]],[.,.]]
 => 4 = 3 + 1
[1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [3,1,2,4] => [[.,.],[.,[.,.]]]
 => 5 = 4 + 1
[1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => [2,1,3,4] => [[.,.],[.,[.,.]]]
 => 5 = 4 + 1
[1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => [.,[.,[.,[.,.]]]]
 => 14 = 13 + 1
[1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]]
 => 2 = 1 + 1
[1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [3,4,2,1,5] => [[[.,[.,.]],.],[.,.]]
 => 4 = 3 + 1
[1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]]
 => 4 = 3 + 1
[1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [3,2,4,1,5] => [[[.,.],[.,.]],[.,.]]
 => 4 = 3 + 1
[1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]]
 => 10 = 9 + 1
[1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [4,3,1,2,5] => [[[.,.],.],[.,[.,.]]]
 => 5 = 4 + 1
[1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]]
 => 10 = 9 + 1
[1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [4,2,1,3,5] => [[[.,.],.],[.,[.,.]]]
 => 5 = 4 + 1
[1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
 => 5 = 4 + 1
[1,1,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]]
 => 10 = 9 + 1
[1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [4,1,2,3,5] => [[.,.],[.,[.,[.,.]]]]
 => 14 = 13 + 1
[1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]]
 => 14 = 13 + 1
[1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
 => 14 = 13 + 1
[1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
 => 42 = 41 + 1
[1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]]
 => 2 = 1 + 1
[1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => [4,5,3,2,1,6] => [[[[.,[.,.]],.],.],[.,.]]
 => 4 = 3 + 1
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [5,3,4,2,1,6] => [[[[.,.],[.,.]],.],[.,.]]
 => 4 = 3 + 1
[1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,0,0]
 => [4,3,5,2,1,6] => [[[[.,.],[.,.]],.],[.,.]]
 => 4 = 3 + 1
[1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [3,4,5,2,1,6] => [[[.,[.,[.,.]]],.],[.,.]]
 => 10 = 9 + 1
[1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => [5,4,2,3,1,6] => [[[[.,.],.],[.,.]],[.,.]]
 => 4 = 3 + 1
[1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [4,5,2,3,1,6] => [[[.,[.,.]],[.,.]],[.,.]]
 => 8 = 7 + 1
[1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,0]
 => [5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]]
 => 4 = 3 + 1
[1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => [4,3,2,5,1,6] => [[[[.,.],.],[.,.]],[.,.]]
 => 4 = 3 + 1
[1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [3,4,2,5,1,6] => [[[.,[.,.]],[.,.]],[.,.]]
 => 8 = 7 + 1
[1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
 => 10 = 9 + 1
[1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => [4,2,3,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
 => 10 = 9 + 1
[1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => [3,2,4,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]]
 => 10 = 9 + 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]]
 => 28 = 27 + 1
[1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [5,4,3,1,2,6] => [[[[.,.],.],.],[.,[.,.]]]
 => 5 = 4 + 1
[1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [4,5,3,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]]
 => 10 = 9 + 1
[1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => [5,3,4,1,2,6] => [[[.,.],[.,.]],[.,[.,.]]]
 => 10 = 9 + 1
[1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,1,0,1,0,0,0]
 => [4,3,5,1,2,6] => [[[.,.],[.,.]],[.,[.,.]]]
 => 10 = 9 + 1
[1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [3,4,5,1,2,6] => [[.,[.,[.,.]]],[.,[.,.]]]
 => 25 = 24 + 1
[1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [5,4,2,1,3,6] => [[[[.,.],.],.],[.,[.,.]]]
 => 5 = 4 + 1
[1,1,0,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,1,0,0,0]
 => [4,5,2,1,3,6] => [[[.,[.,.]],.],[.,[.,.]]]
 => 10 = 9 + 1
[1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [5,3,2,1,4,6] => [[[[.,.],.],.],[.,[.,.]]]
 => 5 = 4 + 1
[1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]]
 => 5 = 4 + 1
[1,1,0,1,0,1,1,0,0,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => [3,4,2,1,5,6] => [[[.,[.,.]],.],[.,[.,.]]]
 => 10 = 9 + 1
[1,1,0,1,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => [5,2,3,1,4,6] => [[[.,.],[.,.]],[.,[.,.]]]
 => 10 = 9 + 1
[1,1,0,1,1,0,0,1,0,0]
 => [1,1,1,0,1,1,0,0,1,0,0,0]
 => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]]
 => 10 = 9 + 1
[1,1,0,1,1,0,1,0,0,0]
 => [1,1,1,0,1,1,0,1,0,0,0,0]
 => [3,2,4,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]]
 => 10 = 9 + 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]]
 => 25 = 24 + 1
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]]
 => ? = 1 + 1
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
 => [5,6,4,3,2,1,7] => [[[[[.,[.,.]],.],.],.],[.,.]]
 => ? = 3 + 1
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
 => [6,4,5,3,2,1,7] => [[[[[.,.],[.,.]],.],.],[.,.]]
 => ? = 3 + 1
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
 => [5,4,6,3,2,1,7] => [[[[[.,.],[.,.]],.],.],[.,.]]
 => ? = 3 + 1
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,1,1,1,0,0,0,0]
 => [4,5,6,3,2,1,7] => [[[[.,[.,[.,.]]],.],.],[.,.]]
 => ? = 9 + 1
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,1,0,0]
 => [6,5,3,4,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]]
 => ? = 3 + 1
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,1,1,0,0,0]
 => [5,6,3,4,2,1,7] => [[[[.,[.,.]],[.,.]],.],[.,.]]
 => ? = 7 + 1
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
 => [6,4,3,5,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]]
 => ? = 3 + 1
[1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => [5,4,3,6,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]]
 => ? = 3 + 1
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,0,1,1,0,1,1,0,0,0,0]
 => [4,5,3,6,2,1,7] => [[[[.,[.,.]],[.,.]],.],[.,.]]
 => ? = 7 + 1
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,1,0,0]
 => [6,3,4,5,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]]
 => ? = 9 + 1
[1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,1,1,1,0,0,1,0,0,0]
 => [5,3,4,6,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]]
 => ? = 9 + 1
[1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,1,0,0,0,0]
 => [4,3,5,6,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]]
 => ? = 9 + 1
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,1,1,1,0,0,0,0,0]
 => [3,4,5,6,2,1,7] => [[[.,[.,[.,[.,.]]]],.],[.,.]]
 => ? = 27 + 1
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,1,0,0]
 => [6,5,4,2,3,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
 => ? = 3 + 1
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,0,1,1,0,0,0]
 => [5,6,4,2,3,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]]
 => ? = 7 + 1
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,1,0,0,1,0,0]
 => [6,4,5,2,3,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
 => ? = 7 + 1
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,1,0,0,0]
 => [5,4,6,2,3,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
 => ? = 7 + 1
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
 => [4,5,6,2,3,1,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]]
 => ? = 19 + 1
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,1,0,0]
 => [6,5,3,2,4,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
 => ? = 3 + 1
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,1,0,0,1,1,0,0,0]
 => [5,6,3,2,4,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]]
 => ? = 7 + 1
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,1,0,0,1,0,0]
 => [6,4,3,2,5,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
 => ? = 3 + 1
[1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => [5,4,3,2,6,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]]
 => ? = 3 + 1
[1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,0,1,1,0,0,0,0]
 => [4,5,3,2,6,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]]
 => ? = 7 + 1
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
 => [6,3,4,2,5,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
 => ? = 7 + 1
[1,0,1,1,0,1,1,0,0,1,0,0]
 => [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
 => [5,3,4,2,6,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
 => ? = 7 + 1
[1,0,1,1,0,1,1,0,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,1,0,0,0,0]
 => [4,3,5,2,6,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]]
 => ? = 7 + 1
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,1,0,1,1,0,1,1,1,0,0,0,0,0]
 => [3,4,5,2,6,1,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]]
 => ? = 19 + 1
[1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,1,0,0]
 => [6,5,2,3,4,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
 => ? = 9 + 1
[1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
 => [5,6,2,3,4,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
 => ? = 19 + 1
[1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,1,0,0,1,0,0,1,0,0]
 => [6,4,2,3,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
 => ? = 9 + 1
[1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,1,0,0,0]
 => [5,4,2,3,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
 => ? = 9 + 1
[1,0,1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,1,1,0,0,0,0]
 => [4,5,2,3,6,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
 => ? = 19 + 1
[1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,1,0,0,0,1,0,0]
 => [6,3,2,4,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
 => ? = 9 + 1
[1,0,1,1,1,0,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,1,0,0,1,0,0,0]
 => [5,3,2,4,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
 => ? = 9 + 1
[1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,1,0,0,0,0]
 => [4,3,2,5,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]]
 => ? = 9 + 1
[1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,1,0,1,1,1,0,1,1,0,0,0,0,0]
 => [3,4,2,5,6,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
 => ? = 19 + 1
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,1,0,0]
 => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
 => ? = 27 + 1
[1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,1,1,1,0,0,0,1,0,0,0]
 => [5,2,3,4,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
 => ? = 27 + 1
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,1,1,0,0,1,0,0,0,0]
 => [4,2,3,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
 => ? = 27 + 1
[1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
 => [3,2,4,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
 => ? = 27 + 1
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => [2,3,4,5,6,1,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
 => ? = 83 + 1
[1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => [6,5,4,3,1,2,7] => [[[[[.,.],.],.],.],[.,[.,.]]]
 => ? = 4 + 1
[1,1,0,0,1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,0,1,1,0,0,0]
 => [5,6,4,3,1,2,7] => [[[[.,[.,.]],.],.],[.,[.,.]]]
 => ? = 9 + 1
[1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,1,1,0,0,1,0,0]
 => [6,4,5,3,1,2,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
 => ? = 9 + 1
[1,1,0,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,1,0,0,0]
 => [5,4,6,3,1,2,7] => [[[[.,.],[.,.]],.],[.,[.,.]]]
 => ? = 9 + 1
[1,1,0,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
 => [4,5,6,3,1,2,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
 => ? = 24 + 1
[1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,1,0,0]
 => [6,5,3,4,1,2,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
 => ? = 9 + 1
[1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,1,1,0,0,0]
 => [5,6,3,4,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
 => ? = 19 + 1
[1,1,0,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,1,0,0,1,0,0]
 => [6,4,3,5,1,2,7] => [[[[.,.],.],[.,.]],[.,[.,.]]]
 => ? = 9 + 1
Description
The number of elements smaller than a binary tree in Tamari order.