- FindStat

Identifier

Mp00100: Dyck paths —touch composition⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St001880: Posets ⟶ ℤ

Values

[1,0,1,0,1,0] => [1,1,1] => [[1,1,1],[]] => ([(0,2),(2,1)],3) => 3

[1,1,0,1,0,0] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3

[1,1,1,0,0,0] => [3] => [[3],[]] => ([(0,2),(2,1)],3) => 3

[1,0,1,0,1,0,1,0] => [1,1,1,1] => [[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => 4

[1,1,0,1,0,1,0,0] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4

[1,1,0,1,1,0,0,0] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4

[1,1,1,0,0,1,0,0] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4

[1,1,1,0,1,0,0,0] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4

[1,1,1,1,0,0,0,0] => [4] => [[4],[]] => ([(0,3),(2,1),(3,2)],4) => 4

[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5

[1,1,0,1,0,1,0,1,0,0] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5

[1,1,0,1,0,1,1,0,0,0] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5

[1,1,0,1,1,0,0,1,0,0] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5

[1,1,0,1,1,0,1,0,0,0] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5

[1,1,0,1,1,1,0,0,0,0] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5

[1,1,1,0,0,1,0,1,0,0] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5

[1,1,1,0,0,1,1,0,0,0] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5

[1,1,1,0,1,0,0,1,0,0] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5

[1,1,1,0,1,0,1,0,0,0] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5

[1,1,1,0,1,1,0,0,0,0] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5

[1,1,1,1,0,0,0,1,0,0] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5

[1,1,1,1,0,0,1,0,0,0] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5

[1,1,1,1,0,1,0,0,0,0] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5

[1,1,1,1,1,0,0,0,0,0] => [5] => [[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5

[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,0,1,0,1,0,1,0,1,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,0,1,0,1,0,1,1,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,0,1,0,1,1,0,0,1,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,0,1,0,1,1,0,1,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,0,1,0,1,1,1,0,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,0,1,1,0,0,1,0,1,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,0,1,1,0,0,1,1,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,0,1,1,0,1,0,0,1,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,0,1,1,0,1,0,1,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,0,1,1,0,1,1,0,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,0,1,1,1,0,0,0,1,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,0,1,1,1,0,0,1,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,0,1,1,1,0,1,0,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,0,1,1,1,1,0,0,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,0,0,1,0,1,0,1,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,0,0,1,0,1,1,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,0,0,1,1,0,0,1,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,0,0,1,1,0,1,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,0,0,1,1,1,0,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,0,1,0,0,1,0,1,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,0,1,0,0,1,1,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,0,1,0,1,0,0,1,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,0,1,0,1,0,1,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,0,1,0,1,1,0,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,0,1,1,0,0,0,1,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,0,1,1,0,0,1,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,0,1,1,0,1,0,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,0,1,1,1,0,0,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,1,0,0,0,1,0,1,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,1,0,0,0,1,1,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,1,0,0,1,0,0,1,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,1,0,0,1,0,1,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,1,0,0,1,1,0,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,1,0,1,0,0,0,1,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,1,0,1,0,0,1,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,1,0,1,0,1,0,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,1,0,1,1,0,0,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,1,1,0,0,0,0,1,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,1,1,0,0,0,1,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,1,1,0,0,1,0,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,1,1,0,1,0,0,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,1,1,1,1,1,0,0,0,0,0,0] => [6] => [[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6

[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

>>> Load all 200 entries. <<<

[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7] => [[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 7

search for individual values

searching the database for the individual values of this statistic

Description

The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.

Map

touch composition

Description

Sends a Dyck path to its touch composition given by the composition of lengths of its touch points.

Map

to ribbon

Description

The ribbon shape corresponding to an integer composition.
For an integer composition

$(a_1, \dots, a_n)$ , this is the ribbon shape whose

$i$ th row from the bottom has

$a_i$ cells.

Map

cell poset

Description

The Young diagram of a skew partition regarded as a poset.
This is the poset on the cells of the Young diagram, such that a cell

$d$ is greater than a cell

$c$ if the entry in

$d$ must be larger than the entry of

$c$ in any standard Young tableau on the skew partition.