- FindStat

Identifier

Mp00018: Binary trees —left border symmetry⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
St001568: Integer partitions ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[.,[[.,[.,.]],[.,.]]] => [.,[[.,[.,.]],[.,.]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => [8] => 1

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

[.,[[.,[.,[.,.]]],.]] => [.,[[.,.],[.,[.,.]]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => [8] => 1

[.,[[.,[[.,.],.]],.]] => [.,[[.,.],[[.,.],.]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => [8] => 1

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

[.,[[[.,[.,.]],.],.]] => [.,[[[.,.],.],[.,.]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => [8] => 1

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

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

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

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

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

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

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

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

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

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

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

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

[[[.,.],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => [8] => 1

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

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

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

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

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

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

[[[.,.],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => [8] => 1

[[[.,.],[[.,.],.]],.] => [[[.,.],[[.,.],.]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => [8] => 1

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

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

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

[[[[.,.],[.,.]],.],.] => [[[[.,.],.],[.,.]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => [8] => 1

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

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

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

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

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

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

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

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

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

[.,[.,[[.,[.,.]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,.]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [9] => 1

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

[.,[.,[[.,[.,[.,.]]],.]]] => [.,[.,[[.,.],[.,[.,.]]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [9] => 1

[.,[.,[[.,[[.,.],.]],.]]] => [.,[.,[[.,.],[[.,.],.]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [9] => 1

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

[.,[.,[[[.,[.,.]],.],.]]] => [.,[.,[[[.,.],.],[.,.]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [9] => 1

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

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

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

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

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

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

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

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

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

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

[.,[[[.,.],[.,.]],[.,.]]] => [.,[[[.,[.,.]],[.,.]],.]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [9] => 1

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

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

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

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

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

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

[.,[[[.,.],[.,[.,.]]],.]] => [.,[[[.,.],[.,[.,.]]],.]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [9] => 1

[.,[[[.,.],[[.,.],.]],.]] => [.,[[[.,.],[[.,.],.]],.]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [9] => 1

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

[.,[[[[.,.],[.,.]],.],.]] => [.,[[[[.,.],.],[.,.]],.]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [9] => 1

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

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

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

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

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

>>> Load all 246 entries. <<<

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

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

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

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

[[.,.],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [9] => 1

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

[[.,.],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [9] => 1

[[.,.],[[.,[[.,.],.]],.]] => [[.,[[.,.],[[.,.],.]]],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [9] => 1

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

[[.,.],[[[.,[.,.]],.],.]] => [[.,[[[.,.],.],[.,.]]],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [9] => 1

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

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

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

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

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

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

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

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

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

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

[[[[.,.],.],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],.],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [9] => 1

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

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

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

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

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

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

[[[[.,.],.],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],.],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [9] => 1

[[[[.,.],.],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],.],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [9] => 1

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

[[[[[.,.],.],[.,.]],.],.] => [[[[[.,.],.],[.,.]],.],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [9] => 1

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

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

[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

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

[.,[.,[.,[.,[[[.,.],.],.]]]]] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[.,[.,[[.,.],[[.,.],.]]]]] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[.,[.,[.,[[[.,.],.],[.,.]]]]] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[.,[.,[.,[[.,[[.,.],.]],.]]]] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

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

[.,[.,[.,[[[.,[.,.]],.],.]]]] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[.,[.,[.,[[[[.,.],.],.],.]]]] => [.,[.,[.,[[[[.,.],.],.],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[.,[[.,.],[.,[[.,.],.]]]]] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[.,[[.,.],[[.,.],[.,.]]]]] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

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

[.,[.,[[.,.],[[[.,.],.],.]]]] => [.,[.,[[.,[[[.,.],.],.]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[.,[[[.,.],.],[.,[.,.]]]]] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[.,[[[.,.],.],[[.,.],.]]]] => [.,[.,[[[.,[[.,.],.]],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[.,[[[.,.],[.,.]],[.,.]]]] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[.,[.,[[[[.,.],.],.],[.,.]]]] => [.,[.,[[[[.,[.,.]],.],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[.,[[[.,.],[.,[.,.]]],.]]] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[.,[.,[[[.,.],[[.,.],.]],.]]] => [.,[.,[[[.,.],[[.,.],.]],.]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

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

[.,[.,[[[[.,.],[.,.]],.],.]]] => [.,[.,[[[[.,.],.],[.,.]],.]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[.,[.,[[[[[.,.],.],.],.],.]]] => [.,[.,[[[[[.,.],.],.],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[[.,.],[.,[.,[[.,.],.]]]]] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[[.,.],[.,[[.,.],[.,.]]]]] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

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

[.,[[.,.],[.,[[[.,.],.],.]]]] => [.,[[.,[.,[[[.,.],.],.]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[[.,.],[[.,.],[.,[.,.]]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[[.,.],[[.,.],[[.,.],.]]]] => [.,[[.,[[.,[[.,.],.]],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[[.,.],[[.,[.,.]],[.,.]]]] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[.,[[.,.],[[[.,.],.],[.,.]]]] => [.,[[.,[[[.,[.,.]],.],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[[.,.],[[.,[.,[.,.]]],.]]] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[.,[[.,.],[[.,[[.,.],.]],.]]] => [.,[[.,[[.,.],[[.,.],.]]],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

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

[.,[[.,.],[[[.,[.,.]],.],.]]] => [.,[[.,[[[.,.],.],[.,.]]],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[.,[[.,.],[[[[.,.],.],.],.]]] => [.,[[.,[[[[.,.],.],.],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[[[.,.],.],[.,[.,[.,.]]]]] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[[[.,.],.],[.,[[.,.],.]]]] => [.,[[[.,[.,[[.,.],.]]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[[[.,.],.],[[.,.],[.,.]]]] => [.,[[[.,[[.,[.,.]],.]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

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

[.,[[[.,.],.],[[[.,.],.],.]]] => [.,[[[.,[[[.,.],.],.]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[[[[.,.],.],.],[.,[.,.]]]] => [.,[[[[.,[.,[.,.]]],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[[[[.,.],.],.],[[.,.],.]]] => [.,[[[[.,[[.,.],.]],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[[[[.,.],.],[.,.]],[.,.]]] => [.,[[[[.,[.,.]],[.,.]],.],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[.,[[[[[.,.],.],.],.],[.,.]]] => [.,[[[[[.,[.,.]],.],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[.,[[[[.,.],.],[.,[.,.]]],.]] => [.,[[[[.,.],[.,[.,.]]],.],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[.,[[[[.,.],.],[[.,.],.]],.]] => [.,[[[[.,.],[[.,.],.]],.],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

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

[.,[[[[[.,.],.],[.,.]],.],.]] => [.,[[[[[.,.],.],[.,.]],.],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[.,[[[[[[.,.],.],.],.],.],.]] => [.,[[[[[[.,.],.],.],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[.,.],[.,[.,[.,[[.,.],.]]]]] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[.,.],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

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

[[.,.],[.,[.,[[[.,.],.],.]]]] => [[.,[.,[.,[[[.,.],.],.]]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[.,.],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[.,.],[.,[[.,.],[[.,.],.]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[.,.],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[[.,.],[.,[[[.,.],.],[.,.]]]] => [[.,[.,[[[.,[.,.]],.],.]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[.,.],[.,[[.,[.,[.,.]]],.]]] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[[.,.],[.,[[.,[[.,.],.]],.]]] => [[.,[.,[[.,.],[[.,.],.]]]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

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

[[.,.],[.,[[[.,[.,.]],.],.]]] => [[.,[.,[[[.,.],.],[.,.]]]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[[.,.],[.,[[[[.,.],.],.],.]]] => [[.,[.,[[[[.,.],.],.],.]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[.,.],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[.,.],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[.,.],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

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

[[.,.],[[.,.],[[[.,.],.],.]]] => [[.,[[.,[[[.,.],.],.]],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[.,.],[[[.,.],.],[.,[.,.]]]] => [[.,[[[.,[.,[.,.]]],.],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[.,.],[[[.,.],.],[[.,.],.]]] => [[.,[[[.,[[.,.],.]],.],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[.,.],[[[.,.],[.,.]],[.,.]]] => [[.,[[[.,[.,.]],[.,.]],.]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[[.,.],[[[[.,.],.],.],[.,.]]] => [[.,[[[[.,[.,.]],.],.],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[.,.],[[[.,.],[.,[.,.]]],.]] => [[.,[[[.,.],[.,[.,.]]],.]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[[.,.],[[[.,.],[[.,.],.]],.]] => [[.,[[[.,.],[[.,.],.]],.]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

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

[[.,.],[[[[.,.],[.,.]],.],.]] => [[.,[[[[.,.],.],[.,.]],.]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[[.,.],[[[[[.,.],.],.],.],.]] => [[.,[[[[[.,.],.],.],.],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[[.,.],.],[.,[.,[.,[.,.]]]]] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[[.,.],.],[.,[.,[[.,.],.]]]] => [[[.,[.,[.,[[.,.],.]]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[[.,.],.],[.,[[.,.],[.,.]]]] => [[[.,[.,[[.,[.,.]],.]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

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

[[[.,.],.],[.,[[[.,.],.],.]]] => [[[.,[.,[[[.,.],.],.]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[[.,.],.],[[.,.],[.,[.,.]]]] => [[[.,[[.,[.,[.,.]]],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[[.,.],.],[[.,.],[[.,.],.]]] => [[[.,[[.,[[.,.],.]],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[[.,.],.],[[.,[.,.]],[.,.]]] => [[[.,[[.,[.,.]],[.,.]]],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[[[.,.],.],[[[.,.],.],[.,.]]] => [[[.,[[[.,[.,.]],.],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[[.,.],.],[[.,[.,[.,.]]],.]] => [[[.,[[.,.],[.,[.,.]]]],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[[[.,.],.],[[.,[[.,.],.]],.]] => [[[.,[[.,.],[[.,.],.]]],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

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

[[[.,.],.],[[[.,[.,.]],.],.]] => [[[.,[[[.,.],.],[.,.]]],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[[[.,.],.],[[[[.,.],.],.],.]] => [[[.,[[[[.,.],.],.],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[[[.,.],.],.],[.,[.,[.,.]]]] => [[[[.,[.,[.,[.,.]]]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[[[.,.],.],.],[.,[[.,.],.]]] => [[[[.,[.,[[.,.],.]]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[[[.,.],.],.],[[.,.],[.,.]]] => [[[[.,[[.,[.,.]],.]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

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

[[[[.,.],.],.],[[[.,.],.],.]] => [[[[.,[[[.,.],.],.]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[[[[.,.],.],.],.],[.,[.,.]]] => [[[[[.,[.,[.,.]]],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[[[[.,.],.],.],.],[[.,.],.]] => [[[[[.,[[.,.],.]],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[[[[.,.],.],.],[.,.]],[.,.]] => [[[[[.,[.,.]],[.,.]],.],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[[[[[[.,.],.],.],.],.],[.,.]] => [[[[[[.,[.,.]],.],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

[[[[[.,.],.],.],[.,[.,.]]],.] => [[[[[.,.],[.,[.,.]]],.],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[[[[[.,.],.],.],[[.,.],.]],.] => [[[[[.,.],[[.,.],.]],.],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

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

[[[[[[.,.],.],.],[.,.]],.],.] => [[[[[[.,.],.],[.,.]],.],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 1

[[[[[[[.,.],.],.],.],.],.],.] => [[[[[[[.,.],.],.],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [8] => 1

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

$F_{1} = q$

$F_{2} = 2\ q$

$F_{3} = 5\ q$

$F_{4} = 14\ q$

Description

The smallest positive integer that does not appear twice in the partition.

Map

left border symmetry

Description

Return the tree where a symmetry has been applied recursively on all left borders. If a tree is made of three trees

$T_1, T_2, T_3$ on its left border, it becomes

$T_3, T_2, T_1$ where same symmetry has been applied to

$T_1, T_2, T_3$ .

Map

rowmotion cycle type

Description

The cycle type of rowmotion on the order ideals of a poset.

Map

to poset

Description

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