Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001267
Mapping
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St001267: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1,0,0,1,0]
 => [[2,2],[1]]
 => [1]
 => 10 => 2
[1,0,1,1,0,0,1,0]
 => [[2,2,1],[1]]
 => [1]
 => 10 => 2
[1,1,0,0,1,0,1,0]
 => [[2,2,2],[1,1]]
 => [1,1]
 => 110 => 3
[1,1,0,0,1,1,0,0]
 => [[3,2],[1]]
 => [1]
 => 10 => 2
[1,1,0,1,0,0,1,0]
 => [[3,3],[2]]
 => [2]
 => 100 => 3
[1,1,0,1,1,0,0,0]
 => [[3,3],[1]]
 => [1]
 => 10 => 2
[1,1,1,0,0,0,1,0]
 => [[2,2,2],[1]]
 => [1]
 => 10 => 2
[1,0,1,0,1,1,0,0,1,0]
 => [[2,2,1,1],[1]]
 => [1]
 => 10 => 2
[1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1],[1,1]]
 => [1,1]
 => 110 => 3
[1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1],[1]]
 => [1]
 => 10 => 2
[1,0,1,1,0,1,0,0,1,0]
 => [[3,3,1],[2]]
 => [2]
 => 100 => 3
[1,0,1,1,0,1,1,0,0,0]
 => [[3,3,1],[1]]
 => [1]
 => 10 => 2
[1,0,1,1,1,0,0,0,1,0]
 => [[2,2,2,1],[1]]
 => [1]
 => 10 => 2
[1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2],[1,1,1]]
 => [1,1,1]
 => 1110 => 4
[1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2],[1,1]]
 => [1,1]
 => 110 => 3
[1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2],[2,1]]
 => [2,1]
 => 1010 => 3
[1,1,0,0,1,1,0,1,0,0]
 => [[4,2],[1]]
 => [1]
 => 10 => 2
[1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2],[1,1]]
 => [1,1]
 => 110 => 3
[1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3],[2,2]]
 => [2,2]
 => 1100 => 4
[1,1,0,1,0,0,1,1,0,0]
 => [[4,3],[2]]
 => [2]
 => 100 => 3
[1,1,0,1,0,1,0,0,1,0]
 => [[4,4],[3]]
 => [3]
 => 1000 => 4
[1,1,0,1,0,1,1,0,0,0]
 => [[4,4],[2]]
 => [2]
 => 100 => 3
[1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3],[2,1]]
 => [2,1]
 => 1010 => 3
[1,1,0,1,1,0,0,1,0,0]
 => [[4,3],[1]]
 => [1]
 => 10 => 2
[1,1,0,1,1,0,1,0,0,0]
 => [[3,3,3],[1,1]]
 => [1,1]
 => 110 => 3
[1,1,0,1,1,1,0,0,0,0]
 => [[4,4],[1]]
 => [1]
 => 10 => 2
[1,1,1,0,0,0,1,0,1,0]
 => [[2,2,2,2],[1,1]]
 => [1,1]
 => 110 => 3
[1,1,1,0,0,0,1,1,0,0]
 => [[3,2,2],[1]]
 => [1]
 => 10 => 2
[1,1,1,0,0,1,0,0,1,0]
 => [[3,3,2],[2]]
 => [2]
 => 100 => 3
[1,1,1,0,0,1,1,0,0,0]
 => [[3,3,2],[1]]
 => [1]
 => 10 => 2
[1,1,1,0,1,0,0,0,1,0]
 => [[2,2,2,2],[1]]
 => [1]
 => 10 => 2
[1,1,1,1,0,0,0,0,1,0]
 => [[3,3,3],[2]]
 => [2]
 => 100 => 3
[1,1,1,1,0,0,1,0,0,0]
 => [[3,3,3],[1]]
 => [1]
 => 10 => 2
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [[2,2,1,1,1],[1]]
 => [1]
 => 10 => 2
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1,1],[1,1]]
 => [1,1]
 => 110 => 3
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1,1],[1]]
 => [1]
 => 10 => 2
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [[3,3,1,1],[2]]
 => [2]
 => 100 => 3
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [[3,3,1,1],[1]]
 => [1]
 => 10 => 2
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [[2,2,2,1,1],[1]]
 => [1]
 => 10 => 2
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2,1],[1,1,1]]
 => [1,1,1]
 => 1110 => 4
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2,1],[1,1]]
 => [1,1]
 => 110 => 3
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2,1],[2,1]]
 => [2,1]
 => 1010 => 3
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [[4,2,1],[1]]
 => [1]
 => 10 => 2
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2,1],[1,1]]
 => [1,1]
 => 110 => 3
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3,1],[2,2]]
 => [2,2]
 => 1100 => 4
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [[4,3,1],[2]]
 => [2]
 => 100 => 3
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [[4,4,1],[3]]
 => [3]
 => 1000 => 4
[1,0,1,1,0,1,0,1,1,0,0,0]
 => [[4,4,1],[2]]
 => [2]
 => 100 => 3
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3,1],[2,1]]
 => [2,1]
 => 1010 => 3
[1,0,1,1,0,1,1,0,0,1,0,0]
 => [[4,3,1],[1]]
 => [1]
 => 10 => 2
Description
The length of the Lyndon factorization of the binary word. The Lyndon factorization of a finite word w is its unique factorization as a non-increasing product of Lyndon words, i.e., $w = l_1\dots l_n$ where each $l_i$ is a Lyndon word and $l_1 \geq\dots\geq l_n$.
Matching statistic: St001232
(load all 3 compositions to match this statistic)
Mapping
Mp00143: Dyck paths —inverse promotion⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 62%
Values
[1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => [1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => 2
[1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 2
[1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
[1,1,0,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 2
[1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
[1,1,0,1,1,0,0,0]
 => [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
[1,1,1,0,0,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 2
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => ? = 2
[1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => ? = 2
[1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => ? = 2
[1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 2
[1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => ? = 4
[1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ? = 3
[1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => ? = 3
[1,1,0,0,1,1,0,1,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ? = 2
[1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => ? = 3
[1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ? = 3
[1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[1,1,0,1,0,1,1,0,0,0]
 => [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
[1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => ? = 3
[1,1,0,1,1,0,0,1,0,0]
 => [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
[1,1,0,1,1,0,1,0,0,0]
 => [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
[1,1,0,1,1,1,0,0,0,0]
 => [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
[1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? = 3
[1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => ? = 2
[1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? = 3
[1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => ? = 2
[1,1,1,0,1,0,0,0,1,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => ? = 2
[1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 3
[1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => ? = 2
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => ? = 2
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => ? = 3
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => ? = 2
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => ? = 3
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 2
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => ? = 2
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => ? = 4
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => ? = 3
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,1,0,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 2
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 3
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => ? = 4
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => ? = 4
[1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 3
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => ? = 3
[1,0,1,1,0,1,1,0,0,1,0,0]
 => [1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 2
[1,0,1,1,0,1,1,0,1,0,0,0]
 => [1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 3
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
[1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 2
[1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,0,0,1,1,0,0,0]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 2
[1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 2
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 3
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 2
[1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
[1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
[1,1,0,1,0,1,0,1,1,0,0,0]
 => [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
[1,1,0,1,0,1,1,0,0,1,0,0]
 => [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
[1,1,0,1,0,1,1,0,1,0,0,0]
 => [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
[1,1,0,1,1,0,0,1,0,1,0,0]
 => [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
[1,1,0,1,1,0,1,0,0,1,0,0]
 => [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
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
 => [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
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
 => [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
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
 => [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
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
 => [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
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
 => [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
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
 => [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]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]
 => [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]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => 3
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001207
Mapping
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 25%
Values
[1,1,0,0,1,0]
 => [2]
 => [1,1,0,0,1,0]
 => [1,3,2] => 1 = 2 - 1
[1,0,1,1,0,0,1,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [2,1,4,3] => 1 = 2 - 1
[1,1,0,0,1,0,1,0]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,3,4,2] => 2 = 3 - 1
[1,1,0,0,1,1,0,0]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,3,2,4] => 1 = 2 - 1
[1,1,0,1,0,0,1,0]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [3,1,4,2] => 2 = 3 - 1
[1,1,0,1,1,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [2,1,3] => 1 = 2 - 1
[1,1,1,0,0,0,1,0]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [1,2,4,3] => 1 = 2 - 1
[1,0,1,0,1,1,0,0,1,0]
 => [4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,0]
 => [2,3,1,5,4] => ? = 2 - 1
[1,0,1,1,0,0,1,0,1,0]
 => [4,3,1,1]
 => [1,0,1,1,0,0,1,0,1,0]
 => [2,1,4,5,3] => ? = 3 - 1
[1,0,1,1,0,0,1,1,0,0]
 => [3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0]
 => [2,1,4,3,5] => ? = 2 - 1
[1,0,1,1,0,1,0,0,1,0]
 => [4,2,1,1]
 => [1,0,1,1,0,1,0,0,1,0]
 => [2,4,1,5,3] => ? = 3 - 1
[1,0,1,1,0,1,1,0,0,0]
 => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [2,4,1,3,5] => ? = 2 - 1
[1,0,1,1,1,0,0,0,1,0]
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [2,1,3,5,4] => ? = 2 - 1
[1,1,0,0,1,0,1,0,1,0]
 => [4,3,2]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,3,4,5,2] => ? = 4 - 1
[1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,3,4,2,5] => ? = 3 - 1
[1,1,0,0,1,1,0,0,1,0]
 => [4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,3,2,5,4] => ? = 3 - 1
[1,1,0,0,1,1,0,1,0,0]
 => [3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [1,3,5,2,4] => ? = 2 - 1
[1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,3,2,4,5] => ? = 3 - 1
[1,1,0,1,0,0,1,0,1,0]
 => [4,3,1]
 => [1,1,0,1,0,0,1,0,1,0]
 => [3,1,4,5,2] => ? = 4 - 1
[1,1,0,1,0,0,1,1,0,0]
 => [3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [3,1,4,2,5] => ? = 3 - 1
[1,1,0,1,0,1,0,0,1,0]
 => [4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [3,4,1,5,2] => ? = 4 - 1
[1,1,0,1,0,1,1,0,0,0]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [2,3,1,4] => 2 = 3 - 1
[1,1,0,1,1,0,0,0,1,0]
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [3,1,2,5,4] => ? = 3 - 1
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [2,1,4,3] => 1 = 2 - 1
[1,1,0,1,1,0,1,0,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [2,4,1,3] => 2 = 3 - 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [2,1,3,4] => 1 = 2 - 1
[1,1,1,0,0,0,1,0,1,0]
 => [4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,2,4,5,3] => ? = 3 - 1
[1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,2,4,3,5] => ? = 2 - 1
[1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,4,2,5,3] => ? = 3 - 1
[1,1,1,0,0,1,1,0,0,0]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,3,2,4] => 1 = 2 - 1
[1,1,1,0,1,0,0,0,1,0]
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [4,1,2,5,3] => ? = 2 - 1
[1,1,1,1,0,0,0,0,1,0]
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,2,3,5,4] => ? = 3 - 1
[1,1,1,1,0,0,1,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [1,3,2] => 1 = 2 - 1
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [5,3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [2,3,4,1,6,5] => ? = 2 - 1
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [5,4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [2,3,1,5,6,4] => ? = 3 - 1
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [4,4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,1,0,0]
 => [2,3,1,5,4,6] => ? = 2 - 1
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [5,3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [2,3,5,1,6,4] => ? = 3 - 1
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [3,3,2,2,1]
 => [1,0,1,0,1,1,0,1,1,0,0,0]
 => [2,3,5,1,4,6] => ? = 2 - 1
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [5,2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [2,3,1,4,6,5] => ? = 2 - 1
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,1]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [2,1,4,5,6,3] => ? = 4 - 1
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [4,4,3,1,1]
 => [1,0,1,1,0,0,1,0,1,1,0,0]
 => [2,1,4,5,3,6] => ? = 3 - 1
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [5,3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,6,5] => ? = 3 - 1
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [4,3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,1,0,0]
 => [2,1,4,6,3,5] => ? = 2 - 1
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [3,3,3,1,1]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [2,1,4,3,5,6] => ? = 3 - 1
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [5,4,2,1,1]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [2,4,1,5,6,3] => ? = 4 - 1
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [4,4,2,1,1]
 => [1,0,1,1,0,1,0,0,1,1,0,0]
 => [2,4,1,5,3,6] => ? = 3 - 1
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [5,3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [2,4,5,1,6,3] => ? = 4 - 1
[1,0,1,1,0,1,0,1,1,0,0,0]
 => [3,3,2,1,1]
 => [1,0,1,1,0,1,0,1,1,0,0,0]
 => [2,4,5,1,3,6] => ? = 3 - 1
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [5,2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [2,4,1,3,6,5] => ? = 3 - 1
[1,0,1,1,0,1,1,0,0,1,0,0]
 => [4,2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,1,0,0]
 => [2,4,1,6,3,5] => ? = 2 - 1
[1,0,1,1,0,1,1,0,1,0,0,0]
 => [3,2,2,1,1]
 => [1,0,1,1,0,1,1,0,1,0,0,0]
 => [2,4,6,1,3,5] => ? = 3 - 1
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [2,2,2,1,1]
 => [1,0,1,1,0,1,1,1,0,0,0,0]
 => [2,4,1,3,5,6] => ? = 2 - 1
[1,0,1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [2,1,3,5,6,4] => ? = 3 - 1
[1,0,1,1,1,0,0,0,1,1,0,0]
 => [4,4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [2,1,3,5,4,6] => ? = 2 - 1
[1,0,1,1,1,0,0,1,0,0,1,0]
 => [5,3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [2,1,5,3,6,4] => ? = 3 - 1
[1,0,1,1,1,0,0,1,1,0,0,0]
 => [3,3,1,1,1]
 => [1,0,1,1,1,0,0,1,1,0,0,0]
 => [2,1,5,3,4,6] => ? = 2 - 1
[1,0,1,1,1,0,1,0,0,0,1,0]
 => [5,2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0,1,0]
 => [2,5,1,3,6,4] => ? = 2 - 1
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [5,1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [2,1,3,4,6,5] => ? = 3 - 1
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [2,1,6,3,4,5] => ? = 2 - 1
[1,1,0,0,1,0,1,0,1,0,1,0]
 => [5,4,3,2]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,3,4,5,6,2] => ? = 5 - 1
[1,1,0,0,1,0,1,0,1,1,0,0]
 => [4,4,3,2]
 => [1,1,0,0,1,0,1,0,1,1,0,0]
 => [1,3,4,5,2,6] => ? = 4 - 1
[1,1,0,0,1,0,1,1,0,0,1,0]
 => [5,3,3,2]
 => [1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,3,4,2,6,5] => ? = 3 - 1
[1,1,0,0,1,0,1,1,0,1,0,0]
 => [4,3,3,2]
 => [1,1,0,0,1,0,1,1,0,1,0,0]
 => [1,3,4,6,2,5] => ? = 3 - 1
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [2,1,4,3] => 1 = 2 - 1
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,3,4,2] => 2 = 3 - 1
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,3,2,4] => 1 = 2 - 1
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [3,1,4,2] => 2 = 3 - 1
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [2,1,3] => 1 = 2 - 1
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [1,2,4,3] => 1 = 2 - 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [2,3,1,4] => 2 = 3 - 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [2,1,4,3] => 1 = 2 - 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [2,4,1,3] => 2 = 3 - 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [2,1,3,4] => 1 = 2 - 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,3,2,4] => 1 = 2 - 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [1,3,2] => 1 = 2 - 1
Description
The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$.