- FindStat

Identifier

Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00140: Dyck paths —logarithmic height to pruning number⟶ Binary trees
Mp00011: Binary trees —to graph⟶ Graphs
St000552: Graphs ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 197 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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$F_{1} = 1$

$F_{2} = 2\ q$

$F_{3} = q + 4\ q^{2}$

$F_{4} = 6\ q^{2} + 8\ q^{3}$

$F_{5} = 2\ q^{2} + 24\ q^{3} + 16\ q^{4}$

$F_{6} = 20\ q^{3} + 80\ q^{4} + 32\ q^{5}$

Description

The number of cut vertices of a graph.
A cut vertex is one whose deletion increases the number of connected components.

Map

to graph

Description

Return the undirected graph obtained from the tree nodes and edges, with leaves being ignored.

Map

prime Dyck path

Description

Return the Dyck path obtained by adding an initial up and a final down step.

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].