Identifier
Values
[.,[.,.]] => ([(0,1)],2) => [2] => [1,0,1,0] => 0
[[.,.],.] => ([(0,1)],2) => [2] => [1,0,1,0] => 0
[.,[.,[.,.]]] => ([(0,2),(2,1)],3) => [3] => [1,0,1,0,1,0] => 0
[.,[[.,.],.]] => ([(0,2),(2,1)],3) => [3] => [1,0,1,0,1,0] => 0
[[.,.],[.,.]] => ([(0,2),(1,2)],3) => [2,1] => [1,0,1,1,0,0] => 1
[[.,[.,.]],.] => ([(0,2),(2,1)],3) => [3] => [1,0,1,0,1,0] => 0
[[[.,.],.],.] => ([(0,2),(2,1)],3) => [3] => [1,0,1,0,1,0] => 0
[.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => [4] => [1,0,1,0,1,0,1,0] => 0
[.,[.,[[.,.],.]]] => ([(0,3),(2,1),(3,2)],4) => [4] => [1,0,1,0,1,0,1,0] => 0
[.,[[.,.],[.,.]]] => ([(0,3),(1,3),(3,2)],4) => [3,1] => [1,0,1,0,1,1,0,0] => 1
[.,[[.,[.,.]],.]] => ([(0,3),(2,1),(3,2)],4) => [4] => [1,0,1,0,1,0,1,0] => 0
[.,[[[.,.],.],.]] => ([(0,3),(2,1),(3,2)],4) => [4] => [1,0,1,0,1,0,1,0] => 0
[[.,.],[.,[.,.]]] => ([(0,3),(1,2),(2,3)],4) => [3,1] => [1,0,1,0,1,1,0,0] => 1
[[.,.],[[.,.],.]] => ([(0,3),(1,2),(2,3)],4) => [3,1] => [1,0,1,0,1,1,0,0] => 1
[[.,[.,.]],[.,.]] => ([(0,3),(1,2),(2,3)],4) => [3,1] => [1,0,1,0,1,1,0,0] => 1
[[[.,.],.],[.,.]] => ([(0,3),(1,2),(2,3)],4) => [3,1] => [1,0,1,0,1,1,0,0] => 1
[[.,[.,[.,.]]],.] => ([(0,3),(2,1),(3,2)],4) => [4] => [1,0,1,0,1,0,1,0] => 0
[[.,[[.,.],.]],.] => ([(0,3),(2,1),(3,2)],4) => [4] => [1,0,1,0,1,0,1,0] => 0
[[[.,.],[.,.]],.] => ([(0,3),(1,3),(3,2)],4) => [3,1] => [1,0,1,0,1,1,0,0] => 1
[[[.,[.,.]],.],.] => ([(0,3),(2,1),(3,2)],4) => [4] => [1,0,1,0,1,0,1,0] => 0
[[[[.,.],.],.],.] => ([(0,3),(2,1),(3,2)],4) => [4] => [1,0,1,0,1,0,1,0] => 0
[.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[.,[.,[.,[[.,.],.]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[.,[.,[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,3),(4,2)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[.,[.,[[.,[.,.]],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[.,[.,[[[.,.],.],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[.,[[.,.],[.,[.,.]]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[.,[[.,.],[[.,.],.]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[.,[[.,[.,.]],[.,.]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[.,[[[.,.],.],[.,.]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[.,[[.,[.,[.,.]]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[.,[[.,[[.,.],.]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[.,[[[.,.],[.,.]],.]] => ([(0,4),(1,4),(2,3),(4,2)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[.,[[[.,[.,.]],.],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[.,[[[[.,.],.],.],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[[.,.],[.,[.,[.,.]]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[[.,.],[.,[[.,.],.]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[[.,.],[[.,.],[.,.]]] => ([(0,4),(1,3),(2,3),(3,4)],5) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[[.,.],[[.,[.,.]],.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[[.,.],[[[.,.],.],.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[[.,[.,.]],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => [3,2] => [1,0,1,1,1,0,0,0] => 1
[[.,[.,.]],[[.,.],.]] => ([(0,3),(1,2),(2,4),(3,4)],5) => [3,2] => [1,0,1,1,1,0,0,0] => 1
[[[.,.],.],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => [3,2] => [1,0,1,1,1,0,0,0] => 1
[[[.,.],.],[[.,.],.]] => ([(0,3),(1,2),(2,4),(3,4)],5) => [3,2] => [1,0,1,1,1,0,0,0] => 1
[[.,[.,[.,.]]],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[[.,[[.,.],.]],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[[[.,.],[.,.]],[.,.]] => ([(0,4),(1,3),(2,3),(3,4)],5) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[[[.,[.,.]],.],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[[[[.,.],.],.],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[[.,[.,[.,[.,.]]]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[[.,[.,[[.,.],.]]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[[.,[[.,.],[.,.]]],.] => ([(0,4),(1,4),(2,3),(4,2)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[[.,[[.,[.,.]],.]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[[.,[[[.,.],.],.]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[[[.,.],[.,[.,.]]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[[[.,.],[[.,.],.]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[[[.,[.,.]],[.,.]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[[[[.,.],.],[.,.]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[[[.,[.,[.,.]]],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[[[.,[[.,.],.]],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[[[[.,.],[.,.]],.],.] => ([(0,4),(1,4),(2,3),(4,2)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[[[[.,[.,.]],.],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[[[[[.,.],.],.],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[.,[.,[.,[.,[[.,.],.]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[.,[.,[.,[[.,[.,.]],.]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[.,[.,[.,[[[.,.],.],.]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[.,[.,[[.,[.,[.,.]]],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[.,[.,[[.,[[.,.],.]],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[.,[.,[[[.,[.,.]],.],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[.,[.,[[[[.,.],.],.],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[.,[[.,[.,.]],[.,[.,.]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[.,[[.,[.,.]],[[.,.],.]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[.,[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[.,[[[.,.],.],[[.,.],.]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[.,[[.,[.,[.,[.,.]]]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[.,[[.,[.,[[.,.],.]]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[.,[[.,[[.,[.,.]],.]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[.,[[.,[[[.,.],.],.]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[.,[[[.,[.,[.,.]]],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[.,[[[.,[[.,.],.]],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[.,[[[[.,[.,.]],.],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[.,[[[[[.,.],.],.],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[.,[.,.]],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[.,[.,.]],[.,[[.,.],.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[.,[.,.]],[[.,.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[[.,[.,.]],[[.,[.,.]],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[.,[.,.]],[[[.,.],.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[[.,.],.],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[[.,.],.],[.,[[.,.],.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[[.,.],.],[[.,.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[[[.,.],.],[[.,[.,.]],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[[.,.],.],[[[.,.],.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[.,[.,[.,.]]],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[.,[.,[.,.]]],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[.,[[.,.],.]],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[.,[[.,.],.]],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[[.,.],[.,.]],[.,[.,.]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[[[.,.],[.,.]],[[.,.],.]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[[[.,[.,.]],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[[.,[.,.]],.],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
>>> Load all 139 entries. <<<
[[[[.,.],.],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[[[.,.],.],.],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[.,[.,[.,[.,[.,.]]]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[.,[.,[.,[[.,.],.]]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[.,[.,[[.,[.,.]],.]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[.,[.,[[[.,.],.],.]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[.,[[.,[.,[.,.]]],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[.,[[.,[[.,.],.]],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[.,[[[.,[.,.]],.],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[.,[[[[.,.],.],.],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[[.,[.,.]],[.,[.,.]]],.] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[[.,[.,.]],[[.,.],.]],.] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[[[.,.],.],[.,[.,.]]],.] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[[[.,.],.],[[.,.],.]],.] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[[.,[.,[.,[.,.]]]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[[.,[.,[[.,.],.]]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[[.,[[.,[.,.]],.]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[[.,[[[.,.],.],.]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[[[.,[.,[.,.]]],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[[[.,[[.,.],.]],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[[[[.,[.,.]],.],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[[[[[.,.],.],.],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[.,[.,[.,.]]],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[.,[.,[.,.]]],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[.,[.,[.,.]]],[[[.,.],.],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[.,[[.,.],.]],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[.,[[.,.],.]],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[.,[[.,.],.]],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[.,[[.,.],.]],[[[.,.],.],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[[.,[.,.]],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[[.,[.,.]],.],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[[.,[.,.]],.],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[[.,[.,.]],.],[[[.,.],.],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[[[.,.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[[[.,.],.],.],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[[[.,.],.],.],[[[.,.],.],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
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Description
Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path.
The modified algebra B is obtained from the stable Auslander algebra kQ/I by deleting all relations which contain walks of length at least three (conjectural this step of deletion is not necessary as the stable higher Auslander algebras might be quadratic) and taking as B then the algebra kQ^(op)/J when J is the quadratic perp of the ideal I.
See www.findstat.org/DyckPaths/NakayamaAlgebras for the definition of Loewy length and Nakayama algebras associated to Dyck paths.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
Greene-Kleitman invariant
Description
The Greene-Kleitman invariant of a poset.
This is the partition $(c_1 - c_0, c_2 - c_1, c_3 - c_2, \ldots)$, where $c_k$ is the maximum cardinality of a union of $k$ chains of the poset. Equivalently, this is the conjugate of the partition $(a_1 - a_0, a_2 - a_1, a_3 - a_2, \ldots)$, where $a_k$ is the maximum cardinality of a union of $k$ antichains of the poset.
Map
to poset
Description
Return the poset obtained by interpreting the tree as a Hasse diagram.