Identifier
Values
[1,2,3] => [1,0,1,0,1,0] => [.,[.,[.,.]]] => ([(0,2),(2,1)],3) => 2
[1,3,2] => [1,0,1,1,0,0] => [.,[[.,.],.]] => ([(0,2),(2,1)],3) => 2
[2,1,3] => [1,1,0,0,1,0] => [[.,[.,.]],.] => ([(0,2),(2,1)],3) => 2
[2,3,1] => [1,1,0,1,0,0] => [[[.,.],.],.] => ([(0,2),(2,1)],3) => 2
[1,2,3,4] => [1,0,1,0,1,0,1,0] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => 3
[1,2,4,3] => [1,0,1,0,1,1,0,0] => [.,[.,[[.,.],.]]] => ([(0,3),(2,1),(3,2)],4) => 3
[1,3,2,4] => [1,0,1,1,0,0,1,0] => [.,[[.,[.,.]],.]] => ([(0,3),(2,1),(3,2)],4) => 3
[1,3,4,2] => [1,0,1,1,0,1,0,0] => [.,[[[.,.],.],.]] => ([(0,3),(2,1),(3,2)],4) => 3
[2,1,3,4] => [1,1,0,0,1,0,1,0] => [[.,[.,[.,.]]],.] => ([(0,3),(2,1),(3,2)],4) => 3
[2,1,4,3] => [1,1,0,0,1,1,0,0] => [[.,[[.,.],.]],.] => ([(0,3),(2,1),(3,2)],4) => 3
[2,3,1,4] => [1,1,0,1,0,0,1,0] => [[[.,[.,.]],.],.] => ([(0,3),(2,1),(3,2)],4) => 3
[2,3,4,1] => [1,1,0,1,0,1,0,0] => [[[[.,.],.],.],.] => ([(0,3),(2,1),(3,2)],4) => 3
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[[.,.],.]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => [.,[.,[[.,[.,.]],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => [.,[.,[[[.,.],.],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => [.,[[.,[.,[.,.]]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => [.,[[.,[[.,.],.]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => [.,[[[.,[.,.]],.],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => [.,[[[[.,.],.],.],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => [[.,[.,[[.,.],.]]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => [[.,[[.,[.,.]],.]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => [[.,[[[.,.],.],.]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => [[[.,[[.,.],.]],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => [[[[.,[.,.]],.],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => [[[[[.,.],.],.],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[[.,[.,.]],.]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[1,2,3,5,6,4] => [1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[[[.,.],.],.]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[[.,[.,[.,.]]],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[[.,[[.,.],.]],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[[[.,[.,.]],.],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[[[[.,.],.],.],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,[.,[.,[.,.]]]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0] => [.,[[.,[.,[[.,.],.]]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,[[.,[.,.]],.]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0] => [.,[[.,[[[.,.],.],.]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0] => [.,[[[.,[.,[.,.]]],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0] => [.,[[[.,[[.,.],.]],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0] => [.,[[[[.,[.,.]],.],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],.],.],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[2,1,3,4,6,5] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[.,[.,[.,[[.,.],.]]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[2,1,3,5,6,4] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[.,[.,[[[.,.],.],.]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,[[.,[.,[.,.]]],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,[[.,[[.,.],.]],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[2,1,4,5,6,3] => [1,1,0,0,1,1,0,1,0,1,0,0] => [[.,[[[[.,.],.],.],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[2,3,1,4,6,5] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[.,[[.,.],.]]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,[.,.]],.]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0] => [[[.,[[[.,.],.],.]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[2,3,4,1,6,5] => [1,1,0,1,0,1,0,0,1,1,0,0] => [[[[.,[[.,.],.]],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => [[[[[.,[.,.]],.],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [[[[[[.,.],.],.],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,2,3,4,5,7,6] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,2,3,4,6,5,7] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,2,3,4,6,7,5] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,2,3,5,4,6,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,2,3,5,4,7,6] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,2,3,5,6,4,7] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,2,3,5,6,7,4] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[[[[.,.],.],.],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,2,4,3,5,6,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,2,4,3,5,7,6] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,2,4,3,6,5,7] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,2,4,3,6,7,5] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [.,[.,[[.,[[[.,.],.],.]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,2,4,5,3,6,7] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,2,4,5,3,7,6] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [.,[.,[[[.,[[.,.],.]],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,2,4,5,6,3,7] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [.,[.,[[[[.,[.,.]],.],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,2,4,5,6,7,3] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[[[[[.,.],.],.],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,3,2,4,5,6,7] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,3,2,4,5,7,6] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,3,2,4,6,5,7] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,3,2,4,6,7,5] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [.,[[.,[.,[[[.,.],.],.]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,3,2,5,4,6,7] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,3,2,5,4,7,6] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [.,[[.,[[.,[[.,.],.]],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,3,2,5,6,4,7] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [.,[[.,[[[.,[.,.]],.],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,3,2,5,6,7,4] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [.,[[.,[[[[.,.],.],.],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,3,4,2,5,6,7] => [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) => 6
[1,3,4,2,5,7,6] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [.,[[[.,[.,[[.,.],.]]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,3,4,2,6,5,7] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [.,[[[.,[[.,[.,.]],.]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,3,4,2,6,7,5] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [.,[[[.,[[[.,.],.],.]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,3,4,5,2,6,7] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [.,[[[[.,[.,[.,.]]],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,3,4,5,2,7,6] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [.,[[[[.,[[.,.],.]],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,3,4,5,6,2,7] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [.,[[[[[.,[.,.]],.],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[1,3,4,5,6,7,2] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],.],.],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,1,3,4,5,7,6] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,1,3,4,6,5,7] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,1,3,4,6,7,5] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[.,[.,[.,[[[.,.],.],.]]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,1,3,5,4,6,7] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,1,3,5,4,7,6] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,[.,[[.,[[.,.],.]],.]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,1,3,5,6,4,7] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[.,[.,[[[.,[.,.]],.],.]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,1,3,5,6,7,4] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[.,[.,[[[[.,.],.],.],.]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,1,4,3,5,6,7] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
>>> Load all 124 entries. <<<
[2,1,4,3,5,7,6] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[.,[[.,[.,[[.,.],.]]],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,1,4,3,6,5,7] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,[[.,[[.,[.,.]],.]],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,1,4,3,6,7,5] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[[.,.],.],.]],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,1,4,5,3,6,7] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[.,[[[.,[.,[.,.]]],.],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,1,4,5,3,7,6] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[.,[[[.,[[.,.],.]],.],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,1,4,5,6,3,7] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,[.,.]],.],.],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,1,4,5,6,7,3] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[[[[[.,.],.],.],.],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,3,1,4,5,6,7] => [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) => 6
[2,3,1,4,5,7,6] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[[.,[.,[.,[[.,.],.]]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,3,1,4,6,5,7] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[[.,[.,[[.,[.,.]],.]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,3,1,4,6,7,5] => [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) => 6
[2,3,1,5,4,6,7] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[[.,[[.,[.,[.,.]]],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,3,1,5,4,7,6] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,[[.,.],.]],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,3,1,5,6,4,7] => [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) => 6
[2,3,1,5,6,7,4] => [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) => 6
[2,3,4,1,5,6,7] => [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) => 6
[2,3,4,1,5,7,6] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[[[.,[.,[[.,.],.]]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,3,4,1,6,5,7] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[[[.,[[.,[.,.]],.]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,3,4,1,6,7,5] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[[[.,[[[.,.],.],.]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,3,4,5,1,6,7] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[[[.,[.,[.,.]]],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,3,4,5,1,7,6] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[[[[.,[[.,.],.]],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,3,4,5,6,1,7] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[[[[.,[.,.]],.],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[2,3,4,5,6,7,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[[[[[.,.],.],.],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
search for individual values
searching the database for the individual values of this statistic
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
Map
to poset
Description
Return the poset obtained by interpreting the tree as a Hasse diagram.
Map
logarithmic height to pruning number
Description
Francon's map from Dyck paths to binary trees.
This bijection sends the logarithmic height of the Dyck path, St000920The logarithmic height of a Dyck path., to the pruning number of the binary tree, St000396The register function (or Horton-Strahler number) of a binary tree.. The implementation is a literal translation of Knuth's [2].
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.