Your data matches 4 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001568
Mapping
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001568: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2],[1,1,1]]
 => [1,1,1]
 => [1,1]
 => 2
[1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3],[2,2]]
 => [2,2]
 => [2]
 => 1
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2,1],[1,1,1]]
 => [1,1,1]
 => [1,1]
 => 2
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3,1],[2,2]]
 => [2,2]
 => [2]
 => 1
[1,1,0,0,1,0,1,0,1,0,1,0]
 => [[2,2,2,2,2],[1,1,1,1]]
 => [1,1,1,1]
 => [1,1,1]
 => 2
[1,1,0,0,1,0,1,0,1,1,0,0]
 => [[3,2,2,2],[1,1,1]]
 => [1,1,1]
 => [1,1]
 => 2
[1,1,0,0,1,0,1,1,0,0,1,0]
 => [[3,3,2,2],[2,1,1]]
 => [2,1,1]
 => [1,1]
 => 2
[1,1,0,0,1,0,1,1,1,0,0,0]
 => [[3,3,2,2],[1,1,1]]
 => [1,1,1]
 => [1,1]
 => 2
[1,1,0,0,1,1,0,0,1,0,1,0]
 => [[3,3,3,2],[2,2,1]]
 => [2,2,1]
 => [2,1]
 => 1
[1,1,0,0,1,1,1,0,0,0,1,0]
 => [[3,3,3,2],[2,1,1]]
 => [2,1,1]
 => [1,1]
 => 2
[1,1,0,0,1,1,1,0,1,0,0,0]
 => [[3,3,3,2],[1,1,1]]
 => [1,1,1]
 => [1,1]
 => 2
[1,1,0,1,0,0,1,0,1,0,1,0]
 => [[3,3,3,3],[2,2,2]]
 => [2,2,2]
 => [2,2]
 => 1
[1,1,0,1,0,0,1,0,1,1,0,0]
 => [[4,3,3],[2,2]]
 => [2,2]
 => [2]
 => 1
[1,1,0,1,0,0,1,1,0,0,1,0]
 => [[4,4,3],[3,2]]
 => [3,2]
 => [2]
 => 1
[1,1,0,1,0,0,1,1,1,0,0,0]
 => [[4,4,3],[2,2]]
 => [2,2]
 => [2]
 => 1
[1,1,0,1,0,1,0,0,1,0,1,0]
 => [[4,4,4],[3,3]]
 => [3,3]
 => [3]
 => 1
[1,1,0,1,0,1,1,0,0,0,1,0]
 => [[4,4,4],[3,2]]
 => [3,2]
 => [2]
 => 1
[1,1,0,1,0,1,1,0,1,0,0,0]
 => [[4,4,4],[2,2]]
 => [2,2]
 => [2]
 => 1
[1,1,0,1,1,0,0,0,1,0,1,0]
 => [[3,3,3,3],[2,2,1]]
 => [2,2,1]
 => [2,1]
 => 1
[1,1,0,1,1,0,1,0,0,0,1,0]
 => [[3,3,3,3],[2,1,1]]
 => [2,1,1]
 => [1,1]
 => 2
[1,1,0,1,1,0,1,0,1,0,0,0]
 => [[3,3,3,3],[1,1,1]]
 => [1,1,1]
 => [1,1]
 => 2
[1,1,1,0,0,0,1,0,1,0,1,0]
 => [[2,2,2,2,2],[1,1,1]]
 => [1,1,1]
 => [1,1]
 => 2
[1,1,1,0,0,1,0,0,1,0,1,0]
 => [[3,3,3,2],[2,2]]
 => [2,2]
 => [2]
 => 1
[1,1,1,1,0,0,0,0,1,0,1,0]
 => [[3,3,3,3],[2,2]]
 => [2,2]
 => [2]
 => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2,1,1],[1,1,1]]
 => [1,1,1]
 => [1,1]
 => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3,1,1],[2,2]]
 => [2,2]
 => [2]
 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [[2,2,2,2,2,1],[1,1,1,1]]
 => [1,1,1,1]
 => [1,1,1]
 => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [[3,2,2,2,1],[1,1,1]]
 => [1,1,1]
 => [1,1]
 => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [[3,3,2,2,1],[2,1,1]]
 => [2,1,1]
 => [1,1]
 => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [[3,3,3,2,1],[2,2,1]]
 => [2,2,1]
 => [2,1]
 => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => [[3,3,3,3,1],[2,2,2]]
 => [2,2,2]
 => [2,2]
 => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
 => [[4,3,3,1],[2,2]]
 => [2,2]
 => [2]
 => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
 => [[4,4,3,1],[3,2]]
 => [3,2]
 => [2]
 => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
 => [[4,4,4,1],[3,3]]
 => [3,3]
 => [3]
 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => [[2,2,2,2,2,2],[1,1,1,1,1]]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
 => [[3,2,2,2,2],[1,1,1,1]]
 => [1,1,1,1]
 => [1,1,1]
 => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
 => [[3,3,2,2,2],[2,1,1,1]]
 => [2,1,1,1]
 => [1,1,1]
 => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
 => [[4,2,2,2],[1,1,1]]
 => [1,1,1]
 => [1,1]
 => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
 => [[3,3,3,2,2],[2,2,1,1]]
 => [2,2,1,1]
 => [2,1,1]
 => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
 => [[4,3,2,2],[2,1,1]]
 => [2,1,1]
 => [1,1]
 => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
 => [[4,4,2,2],[3,1,1]]
 => [3,1,1]
 => [1,1]
 => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
 => [[3,3,3,3,2],[2,2,2,1]]
 => [2,2,2,1]
 => [2,2,1]
 => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
 => [[4,3,3,2],[2,2,1]]
 => [2,2,1]
 => [2,1]
 => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [[4,4,3,2],[3,2,1]]
 => [3,2,1]
 => [2,1]
 => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
 => [[4,4,4,2],[3,3,1]]
 => [3,3,1]
 => [3,1]
 => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [[4,4,4,2],[1,1,1]]
 => [1,1,1]
 => [1,1]
 => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => [[3,3,3,3,3],[2,2,2,2]]
 => [2,2,2,2]
 => [2,2,2]
 => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
 => [[4,3,3,3],[2,2,2]]
 => [2,2,2]
 => [2,2]
 => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
 => [[4,4,3,3],[3,2,2]]
 => [3,2,2]
 => [2,2]
 => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
 => [[5,3,3],[2,2]]
 => [2,2]
 => [2]
 => 1
Description
The smallest positive integer that does not appear twice in the partition.
Matching statistic: St001491
Mapping
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St001491: Binary words ⟶ ℤResult quality: 18% ●values known / values provided: 18%●distinct values known / distinct values provided: 67%
Values
[1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2],[1,1,1]]
 => [1,1,1]
 => 1110 => 2
[1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3],[2,2]]
 => [2,2]
 => 1100 => 1
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2,1],[1,1,1]]
 => [1,1,1]
 => 1110 => 2
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3,1],[2,2]]
 => [2,2]
 => 1100 => 1
[1,1,0,0,1,0,1,0,1,0,1,0]
 => [[2,2,2,2,2],[1,1,1,1]]
 => [1,1,1,1]
 => 11110 => ? = 2
[1,1,0,0,1,0,1,0,1,1,0,0]
 => [[3,2,2,2],[1,1,1]]
 => [1,1,1]
 => 1110 => 2
[1,1,0,0,1,0,1,1,0,0,1,0]
 => [[3,3,2,2],[2,1,1]]
 => [2,1,1]
 => 10110 => ? = 2
[1,1,0,0,1,0,1,1,1,0,0,0]
 => [[3,3,2,2],[1,1,1]]
 => [1,1,1]
 => 1110 => 2
[1,1,0,0,1,1,0,0,1,0,1,0]
 => [[3,3,3,2],[2,2,1]]
 => [2,2,1]
 => 11010 => ? = 1
[1,1,0,0,1,1,1,0,0,0,1,0]
 => [[3,3,3,2],[2,1,1]]
 => [2,1,1]
 => 10110 => ? = 2
[1,1,0,0,1,1,1,0,1,0,0,0]
 => [[3,3,3,2],[1,1,1]]
 => [1,1,1]
 => 1110 => 2
[1,1,0,1,0,0,1,0,1,0,1,0]
 => [[3,3,3,3],[2,2,2]]
 => [2,2,2]
 => 11100 => ? = 1
[1,1,0,1,0,0,1,0,1,1,0,0]
 => [[4,3,3],[2,2]]
 => [2,2]
 => 1100 => 1
[1,1,0,1,0,0,1,1,0,0,1,0]
 => [[4,4,3],[3,2]]
 => [3,2]
 => 10100 => ? = 1
[1,1,0,1,0,0,1,1,1,0,0,0]
 => [[4,4,3],[2,2]]
 => [2,2]
 => 1100 => 1
[1,1,0,1,0,1,0,0,1,0,1,0]
 => [[4,4,4],[3,3]]
 => [3,3]
 => 11000 => ? = 1
[1,1,0,1,0,1,1,0,0,0,1,0]
 => [[4,4,4],[3,2]]
 => [3,2]
 => 10100 => ? = 1
[1,1,0,1,0,1,1,0,1,0,0,0]
 => [[4,4,4],[2,2]]
 => [2,2]
 => 1100 => 1
[1,1,0,1,1,0,0,0,1,0,1,0]
 => [[3,3,3,3],[2,2,1]]
 => [2,2,1]
 => 11010 => ? = 1
[1,1,0,1,1,0,1,0,0,0,1,0]
 => [[3,3,3,3],[2,1,1]]
 => [2,1,1]
 => 10110 => ? = 2
[1,1,0,1,1,0,1,0,1,0,0,0]
 => [[3,3,3,3],[1,1,1]]
 => [1,1,1]
 => 1110 => 2
[1,1,1,0,0,0,1,0,1,0,1,0]
 => [[2,2,2,2,2],[1,1,1]]
 => [1,1,1]
 => 1110 => 2
[1,1,1,0,0,1,0,0,1,0,1,0]
 => [[3,3,3,2],[2,2]]
 => [2,2]
 => 1100 => 1
[1,1,1,1,0,0,0,0,1,0,1,0]
 => [[3,3,3,3],[2,2]]
 => [2,2]
 => 1100 => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2,1,1],[1,1,1]]
 => [1,1,1]
 => 1110 => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3,1,1],[2,2]]
 => [2,2]
 => 1100 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [[2,2,2,2,2,1],[1,1,1,1]]
 => [1,1,1,1]
 => 11110 => ? = 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [[3,2,2,2,1],[1,1,1]]
 => [1,1,1]
 => 1110 => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [[3,3,2,2,1],[2,1,1]]
 => [2,1,1]
 => 10110 => ? = 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [[3,3,3,2,1],[2,2,1]]
 => [2,2,1]
 => 11010 => ? = 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => [[3,3,3,3,1],[2,2,2]]
 => [2,2,2]
 => 11100 => ? = 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
 => [[4,3,3,1],[2,2]]
 => [2,2]
 => 1100 => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
 => [[4,4,3,1],[3,2]]
 => [3,2]
 => 10100 => ? = 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
 => [[4,4,4,1],[3,3]]
 => [3,3]
 => 11000 => ? = 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => [[2,2,2,2,2,2],[1,1,1,1,1]]
 => [1,1,1,1,1]
 => 111110 => ? = 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
 => [[3,2,2,2,2],[1,1,1,1]]
 => [1,1,1,1]
 => 11110 => ? = 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
 => [[3,3,2,2,2],[2,1,1,1]]
 => [2,1,1,1]
 => 101110 => ? = 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
 => [[4,2,2,2],[1,1,1]]
 => [1,1,1]
 => 1110 => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
 => [[3,3,3,2,2],[2,2,1,1]]
 => [2,2,1,1]
 => 110110 => ? = 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
 => [[4,3,2,2],[2,1,1]]
 => [2,1,1]
 => 10110 => ? = 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
 => [[4,4,2,2],[3,1,1]]
 => [3,1,1]
 => 100110 => ? = 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
 => [[3,3,3,3,2],[2,2,2,1]]
 => [2,2,2,1]
 => 111010 => ? = 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
 => [[4,3,3,2],[2,2,1]]
 => [2,2,1]
 => 11010 => ? = 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [[4,4,3,2],[3,2,1]]
 => [3,2,1]
 => 101010 => ? = 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
 => [[4,4,4,2],[3,3,1]]
 => [3,3,1]
 => 110010 => ? = 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [[4,4,4,2],[1,1,1]]
 => [1,1,1]
 => 1110 => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => [[3,3,3,3,3],[2,2,2,2]]
 => [2,2,2,2]
 => 111100 => ? = 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
 => [[4,3,3,3],[2,2,2]]
 => [2,2,2]
 => 11100 => ? = 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
 => [[4,4,3,3],[3,2,2]]
 => [3,2,2]
 => 101100 => ? = 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
 => [[5,3,3],[2,2]]
 => [2,2]
 => 1100 => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
 => [[4,4,4,3],[3,3,2]]
 => [3,3,2]
 => 110100 => ? = 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
 => [[5,4,3],[3,2]]
 => [3,2]
 => 10100 => ? = 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
 => [[5,5,3],[4,2]]
 => [4,2]
 => 100100 => ? = 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => [[4,4,4,4],[3,3,3]]
 => [3,3,3]
 => 111000 => ? = 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
 => [[5,4,4],[3,3]]
 => [3,3]
 => 11000 => ? = 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
 => [[5,5,4],[4,3]]
 => [4,3]
 => 101000 => ? = 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => [[5,5,5],[4,4]]
 => [4,4]
 => 110000 => ? = 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
 => [[5,5,5],[4,3]]
 => [4,3]
 => 101000 => ? = 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
 => [[5,5,5],[3,3]]
 => [3,3]
 => 11000 => ? = 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
 => [[4,4,4,4],[3,3,2]]
 => [3,3,2]
 => 110100 => ? = 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
 => [[5,5,4],[3,2]]
 => [3,2]
 => 10100 => ? = 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
 => [[4,4,4,4],[3,2,2]]
 => [3,2,2]
 => 101100 => ? = 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
 => [[5,4,4],[2,2]]
 => [2,2]
 => 1100 => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => [[4,4,4,4],[2,2,2]]
 => [2,2,2]
 => 11100 => ? = 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
 => [[5,5,4],[2,2]]
 => [2,2]
 => 1100 => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
 => [[5,5,5],[4,2]]
 => [4,2]
 => 100100 => ? = 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
 => [[5,5,5],[3,2]]
 => [3,2]
 => 10100 => ? = 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
 => [[5,5,5],[2,2]]
 => [2,2]
 => 1100 => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
 => [[3,3,3,3,3],[2,2,2,1]]
 => [2,2,2,1]
 => 111010 => ? = 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
 => [[4,4,4,3],[2,2,1]]
 => [2,2,1]
 => 11010 => ? = 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
 => [[3,3,3,3,3],[2,2,1,1]]
 => [2,2,1,1]
 => 110110 => ? = 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
 => [[4,4,3,3],[2,1,1]]
 => [2,1,1]
 => 10110 => ? = 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
 => [[3,3,3,3,3],[2,1,1,1]]
 => [2,1,1,1]
 => 101110 => ? = 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
 => [[4,3,3,3],[1,1,1]]
 => [1,1,1]
 => 1110 => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => [[3,3,3,3,3],[1,1,1,1]]
 => [1,1,1,1]
 => 11110 => ? = 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
 => [[4,4,3,3],[1,1,1]]
 => [1,1,1]
 => 1110 => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
 => [[4,4,4,3],[1,1,1]]
 => [1,1,1]
 => 1110 => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
 => [[4,4,4,4],[1,1,1]]
 => [1,1,1]
 => 1110 => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
 => [[4,4,4,2],[2,2]]
 => [2,2]
 => 1100 => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
 => [[3,3,3,3,2],[1,1,1]]
 => [1,1,1]
 => 1110 => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
 => [[2,2,2,2,2,2],[1,1,1]]
 => [1,1,1]
 => 1110 => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
 => [[4,4,4,3],[2,2]]
 => [2,2]
 => 1100 => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
 => [[3,3,3,3,3],[1,1,1]]
 => [1,1,1]
 => 1110 => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
 => [[4,4,4,4],[2,2]]
 => [2,2]
 => 1100 => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => [[3,3,3,3,3],[2,2]]
 => [2,2]
 => 1100 => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2,1,1,1],[1,1,1]]
 => [1,1,1]
 => 1110 => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [[3,2,2,2,1,1],[1,1,1]]
 => [1,1,1]
 => 1110 => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]
 => [[4,3,3,1,1],[2,2]]
 => [2,2]
 => 1100 => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
 => [[5,3,3,1],[2,2]]
 => [2,2]
 => 1100 => 1
Description
The number of indecomposable projective-injective modules in the algebra corresponding to a subset. Let $A_n=K[x]/(x^n)$. We associate to a nonempty subset S of an (n-1)-set the module $M_S$, which is the direct sum of $A_n$-modules with indecomposable non-projective direct summands of dimension $i$ when $i$ is in $S$ (note that such modules have vector space dimension at most n-1). Then the corresponding algebra associated to S is the stable endomorphism ring of $M_S$. We decode the subset as a binary word so that for example the subset $S=\{1,3 \} $ of $\{1,2,3 \}$ is decoded as 101.
Matching statistic: St000100
Mapping
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
Mp00232: Dyck paths —parallelogram poset⟶ Posets
St000100: Posets ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 33%
Values
[1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1 = 2 - 1
[1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ? = 1 - 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]
 => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1 = 2 - 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]
 => [1,0,1,1,1,0,1,0,0,0,1,0,1,0]
 => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
 => ? = 1 - 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]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1 = 2 - 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]
 => [1,1,0,1,0,0,1,0,1,1,0,1,0,0]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1 = 2 - 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]
 => [1,1,0,1,0,0,1,1,0,1,0,0,1,0]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1 = 2 - 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]
 => [1,1,0,1,0,0,1,1,0,1,0,1,0,0]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1 = 2 - 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]
 => [1,1,0,1,1,0,0,1,0,0,1,0,1,0]
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ? = 1 - 1
[1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0,1,0]
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ? = 2 - 1
[1,1,0,0,1,1,1,0,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,1,0,0,1,0,1,0,1,0,0]
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ? = 2 - 1
[1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0,1,0]
 => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
 => ? = 1 - 1
[1,1,0,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,1,1,0,0,0]
 => [1,1,1,0,1,0,0,0,1,1,0,1,0,0]
 => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
 => ? = 1 - 1
[1,1,0,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,1,0,0,1,0,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0,1,0]
 => ([(0,4),(0,6),(1,8),(3,7),(4,9),(5,2),(6,3),(6,9),(7,8),(8,5),(9,1),(9,7)],10)
 => ? = 1 - 1
[1,1,0,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,0,1,1,1,0,0,0,0]
 => [1,1,1,0,1,1,0,0,0,1,0,1,0,0]
 => ([(0,4),(0,6),(1,8),(3,7),(4,9),(5,2),(6,3),(6,9),(7,8),(8,5),(9,1),(9,7)],10)
 => ? = 1 - 1
[1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
 => ([(0,3),(0,6),(2,8),(3,7),(4,2),(4,9),(5,1),(6,4),(6,7),(7,9),(8,5),(9,8)],10)
 => ? = 1 - 1
[1,1,0,1,0,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,1,1,0,0,0,1,0,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0,1,0]
 => ([(0,3),(0,6),(2,8),(3,7),(4,2),(4,9),(5,1),(6,4),(6,7),(7,9),(8,5),(9,8)],10)
 => ? = 1 - 1
[1,1,0,1,0,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,1,0,1,0,0]
 => ([(0,3),(0,6),(2,8),(3,7),(4,2),(4,9),(5,1),(6,4),(6,7),(7,9),(8,5),(9,8)],10)
 => ? = 1 - 1
[1,1,0,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,1,0,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0,1,0]
 => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
 => ? = 1 - 1
[1,1,0,1,1,0,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,1,0,0,0,1,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0,1,0]
 => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
 => ? = 2 - 1
[1,1,0,1,1,0,1,0,1,0,0,0]
 => [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
 => ? = 2 - 1
[1,1,1,0,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1 = 2 - 1
[1,1,1,0,0,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0,1,0,1,0]
 => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
 => ? = 1 - 1
[1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0,1,0]
 => ([(0,3),(0,6),(2,8),(3,7),(4,2),(4,9),(5,1),(6,4),(6,7),(7,9),(8,5),(9,8)],10)
 => ? = 1 - 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]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => 1 = 2 - 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]
 => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
 => ([(0,6),(2,9),(3,8),(4,2),(4,8),(5,1),(6,7),(7,3),(7,4),(8,9),(9,5)],10)
 => ? = 1 - 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]
 => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => 1 = 2 - 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]
 => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => 1 = 2 - 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]
 => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => 1 = 2 - 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]
 => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ? = 1 - 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
 => ([(0,7),(1,9),(3,8),(4,2),(5,1),(5,8),(6,4),(7,3),(7,5),(8,9),(9,6)],10)
 => ? = 1 - 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
 => [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]
 => ([(0,7),(1,9),(3,8),(4,2),(5,1),(5,8),(6,4),(7,3),(7,5),(8,9),(9,6)],10)
 => ? = 1 - 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]
 => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]
 => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11)
 => ? = 1 - 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
 => ([(0,7),(2,8),(3,9),(4,5),(4,8),(5,3),(5,10),(6,1),(7,2),(7,4),(8,10),(9,6),(10,9)],11)
 => ? = 1 - 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => 1 = 2 - 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => 1 = 2 - 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => 1 = 2 - 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]
 => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
 => ([(0,6),(1,9),(2,8),(3,4),(4,7),(5,1),(5,8),(6,3),(7,2),(7,5),(8,9)],10)
 => ? = 2 - 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => 1 = 2 - 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
 => [1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]
 => ([(0,6),(1,8),(2,8),(4,5),(5,7),(6,4),(7,1),(7,2),(8,3)],9)
 => ? = 2 - 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]
 => ([(0,6),(1,9),(3,8),(4,7),(5,1),(5,8),(6,4),(7,3),(7,5),(8,9),(9,2)],10)
 => ? = 2 - 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
 => ([(0,7),(2,8),(3,8),(4,5),(5,1),(6,4),(7,2),(7,3),(8,6)],9)
 => ? = 1 - 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
 => ([(0,7),(2,8),(3,8),(4,5),(5,1),(6,4),(7,2),(7,3),(8,6)],9)
 => ? = 1 - 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
 => ([(0,7),(1,9),(2,9),(4,8),(5,8),(6,3),(7,1),(7,2),(8,6),(9,4),(9,5)],10)
 => ? = 1 - 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]
 => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11)
 => ? = 1 - 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
 => ([(0,7),(1,8),(2,9),(3,11),(4,3),(4,8),(5,2),(5,10),(6,5),(6,12),(7,1),(7,4),(8,6),(8,11),(10,9),(11,12),(12,10)],13)
 => ? = 2 - 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
 => ([(0,3),(0,7),(2,9),(3,8),(4,6),(5,4),(6,1),(7,2),(7,8),(8,9),(9,5)],10)
 => ? = 1 - 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
 => [1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]
 => ([(0,3),(0,7),(2,9),(3,8),(4,6),(5,4),(6,1),(7,2),(7,8),(8,9),(9,5)],10)
 => ? = 1 - 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]
 => ([(0,3),(0,7),(2,9),(3,8),(4,6),(5,4),(6,1),(7,2),(7,8),(8,9),(9,5)],10)
 => ? = 1 - 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
 => ([(0,4),(0,6),(1,11),(2,10),(3,9),(4,8),(5,2),(5,9),(6,1),(6,8),(7,3),(7,5),(8,11),(9,10),(11,7)],12)
 => ? = 1 - 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]
 => ([(0,4),(0,7),(1,9),(3,8),(4,10),(5,2),(6,5),(7,3),(7,10),(8,9),(9,6),(10,1),(10,8)],11)
 => ? = 1 - 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
 => ([(0,6),(0,7),(1,8),(2,9),(3,9),(5,11),(6,10),(7,1),(7,10),(8,11),(9,4),(10,5),(10,8),(11,2),(11,3)],12)
 => ? = 1 - 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
 => ([(0,5),(0,7),(1,13),(3,12),(4,10),(5,11),(6,3),(6,8),(7,6),(7,11),(8,10),(8,12),(9,13),(10,9),(11,4),(11,8),(12,1),(12,9),(13,2)],14)
 => ? = 1 - 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
 => ([(0,3),(0,7),(2,10),(3,8),(4,5),(5,1),(6,2),(6,9),(7,6),(7,8),(8,9),(9,10),(10,4)],11)
 => ? = 1 - 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
 => ([(0,3),(0,7),(2,10),(3,8),(4,5),(5,1),(6,2),(6,9),(7,6),(7,8),(8,9),(9,10),(10,4)],11)
 => ? = 1 - 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]
 => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
 => ([(0,4),(0,7),(2,9),(3,10),(4,12),(5,3),(5,8),(6,1),(7,5),(7,12),(8,9),(8,10),(9,11),(10,11),(11,6),(12,2),(12,8)],13)
 => ? = 1 - 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
 => ([(0,6),(0,7),(2,9),(3,10),(4,1),(5,3),(5,11),(6,5),(6,8),(7,2),(7,8),(8,9),(8,11),(9,12),(10,13),(11,10),(11,12),(12,13),(13,4)],14)
 => ? = 1 - 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
 => ([(0,6),(0,7),(2,9),(3,10),(4,1),(5,3),(5,11),(6,5),(6,8),(7,2),(7,8),(8,9),(8,11),(9,12),(10,13),(11,10),(11,12),(12,13),(13,4)],14)
 => ? = 1 - 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
 => ([(0,6),(0,7),(2,9),(3,10),(4,1),(5,3),(5,11),(6,5),(6,8),(7,2),(7,8),(8,9),(8,11),(9,12),(10,13),(11,10),(11,12),(12,13),(13,4)],14)
 => ? = 1 - 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]
 => ([(0,3),(0,7),(2,10),(3,8),(4,5),(5,1),(6,2),(6,9),(7,6),(7,8),(8,9),(9,10),(10,4)],11)
 => ? = 1 - 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
 => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
 => [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
 => ([(0,5),(0,7),(1,13),(3,12),(4,10),(5,11),(6,4),(6,8),(7,6),(7,11),(8,10),(8,12),(9,13),(10,9),(11,3),(11,8),(12,1),(12,9),(13,2)],14)
 => ? = 1 - 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
 => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
 => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
 => ([(0,3),(0,7),(2,10),(3,8),(4,5),(5,1),(6,2),(6,9),(7,6),(7,8),(8,9),(9,10),(10,4)],11)
 => ? = 1 - 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
 => ([(0,4),(0,7),(1,10),(2,12),(3,8),(4,9),(5,2),(5,11),(6,1),(6,8),(7,5),(7,9),(8,10),(9,11),(11,12),(12,3),(12,6)],13)
 => ? = 1 - 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
 => ([(0,3),(0,7),(2,10),(3,8),(4,5),(5,1),(6,2),(6,9),(7,6),(7,8),(8,9),(9,10),(10,4)],11)
 => ? = 1 - 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
 => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
 => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
 => ([(0,4),(0,7),(1,9),(2,11),(3,10),(4,14),(5,3),(5,8),(6,1),(6,12),(7,5),(7,14),(8,10),(8,11),(10,13),(11,6),(11,13),(12,9),(13,12),(14,2),(14,8)],15)
 => ? = 1 - 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => 1 = 2 - 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => 1 = 2 - 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
 => 1 = 2 - 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
 => 1 = 2 - 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
 => 1 = 2 - 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
 => 1 = 2 - 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
 => 1 = 2 - 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
 => 1 = 2 - 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
 => 1 = 2 - 1
Description
The number of linear extensions of a poset.
Matching statistic: St001503
Mapping
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
St001503: Dyck paths ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 67%
Values
[1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => 3 = 2 + 1
[1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 2 = 1 + 1
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => 3 = 2 + 1
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => 2 = 1 + 1
[1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 3 = 2 + 1
[1,1,0,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
[1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 3 = 2 + 1
[1,1,0,0,1,0,1,1,1,0,0,0]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => 3 = 2 + 1
[1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 2 = 1 + 1
[1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => 3 = 2 + 1
[1,1,0,0,1,1,1,0,1,0,0,0]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => 3 = 2 + 1
[1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 2 = 1 + 1
[1,1,0,1,0,0,1,0,1,1,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => 2 = 1 + 1
[1,1,0,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => 2 = 1 + 1
[1,1,0,1,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,1,0,0]
 => 2 = 1 + 1
[1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => 2 = 1 + 1
[1,1,0,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => 2 = 1 + 1
[1,1,0,1,0,1,1,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,1,0,1,0,1,1,0,1,0,0,0]
 => 2 = 1 + 1
[1,1,0,1,1,0,0,0,1,0,1,0]
 => [1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => 2 = 1 + 1
[1,1,0,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,1,0,1,0,1,1,0,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => 3 = 2 + 1
[1,1,0,1,1,0,1,0,1,0,0,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => 3 = 2 + 1
[1,1,1,0,0,0,1,0,1,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => 3 = 2 + 1
[1,1,1,0,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => 2 = 1 + 1
[1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => 2 = 1 + 1
[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]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => ? = 2 + 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,1,1,0,0,0,0]
 => ? = 1 + 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [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]
 => ? = 2 + 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,1,0,0]
 => ? = 2 + 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,1,0,0]
 => ? = 2 + 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,1,0,0]
 => ? = 1 + 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 1 + 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
 => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,1,0,0,0]
 => ? = 1 + 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,1,0,1,0,0,1,0,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,1,0,0,0]
 => ? = 1 + 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
 => [1,1,1,0,1,0,1,0,1,1,0,0,0,0]
 => ? = 1 + 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 2 + 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0,1,0]
 => ? = 2 + 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 2 + 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0,1,0]
 => ? = 2 + 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
 => [1,1,1,1,0,1,0,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0,1,0]
 => ? = 2 + 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 1 + 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0,1,0]
 => ? = 1 + 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,1,1,1,0,1,0,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
 => ? = 1 + 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0,1,0]
 => ? = 1 + 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => ? = 2 + 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
 => [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]
 => [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
 => ? = 1 + 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,1,0,0,1,0,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
 => ? = 1 + 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
 => [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]
 => [1,1,1,1,0,1,0,0,0,1,0,1,0,0]
 => ? = 1 + 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,1,0,1,0,1,0,0,1,0,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
 => ? = 1 + 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,1,0,0,1,0,0]
 => ? = 1 + 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,1,1,0,1,0,0,0,1,0,0,0]
 => [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
 => ? = 1 + 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
 => ? = 1 + 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
 => [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]
 => [1,1,1,1,0,1,0,0,1,0,1,0,0,0]
 => ? = 1 + 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,1,1,0,1,0,0,1,0,0,0,0]
 => [1,1,1,1,0,1,0,1,0,0,1,0,0,0]
 => ? = 1 + 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
 => [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => ? = 1 + 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
 => [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => ? = 1 + 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,1,1,0,0,0,0,0]
 => [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
 => ? = 1 + 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => ? = 1 + 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,1,1,0,0,1,0,0]
 => [1,1,1,0,1,1,1,0,0,1,0,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,1,0,0,0]
 => ? = 1 + 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 1 + 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,1,1,0,1,0,0,0]
 => ? = 1 + 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,1,0,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
 => ? = 1 + 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
 => ? = 1 + 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,1,1,0,1,1,1,0,1,0,0,0,0,0]
 => [1,1,0,1,1,1,0,1,0,1,0,0,0,0]
 => ? = 1 + 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,1,1,0,1,0,0,0]
 => [1,1,1,0,1,1,0,1,1,0,0,0,0,0]
 => [1,1,0,1,1,0,1,1,0,1,0,0,0,0]
 => ? = 1 + 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,0,1,0,1,1,1,0,0,0,0,0]
 => [1,1,0,1,0,1,1,1,0,1,0,0,0,0]
 => ? = 1 + 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
 => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1 + 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
 => [1,0,1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,1,1,0,1,0,0,1,0,0]
 => ? = 1 + 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
 => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
 => [1,0,1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,1,0,0,0]
 => [1,0,1,1,0,1,1,0,0,1,0,1,0,0]
 => ? = 2 + 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 2 + 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,0,1,0,1,1,0,1,0,0]
 => ? = 2 + 1
Description
The largest distance of a vertex to a vertex in a cycle in the resolution quiver of the corresponding Nakayama algebra.