- FindStat

Identifier

Mp00013: Binary trees —to poset⟶ Posets
Mp00125: Posets —dual poset⟶ Posets
Mp00282: Posets —Dedekind-MacNeille completion⟶ Lattices
St001878: Lattices ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.

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to poset

Description

Return the poset obtained by interpreting the tree as a Hasse diagram.

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dual poset

Description

The dual of a poset.
The dual (or opposite) of a poset $(\mathcal P,\leq)$ is the poset $(\mathcal P^d,\leq_d)$ with $x \leq_d y$ if $y \leq x$.

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Dedekind-MacNeille completion

Description

Return the smallest lattice containing the poset.