Identifier
-
Mp00072:
Permutations
—binary search tree: left to right⟶
Binary trees
St000128: Binary trees ⟶ ℤ
Values
[1] => [.,.] => 0
[1,2] => [.,[.,.]] => 0
[2,1] => [[.,.],.] => 0
[1,2,3] => [.,[.,[.,.]]] => 0
[1,3,2] => [.,[[.,.],.]] => 0
[2,1,3] => [[.,.],[.,.]] => 0
[2,3,1] => [[.,.],[.,.]] => 0
[3,1,2] => [[.,[.,.]],.] => 0
[3,2,1] => [[[.,.],.],.] => 0
[1,2,3,4] => [.,[.,[.,[.,.]]]] => 0
[1,2,4,3] => [.,[.,[[.,.],.]]] => 0
[1,3,2,4] => [.,[[.,.],[.,.]]] => 0
[1,3,4,2] => [.,[[.,.],[.,.]]] => 0
[1,4,2,3] => [.,[[.,[.,.]],.]] => 0
[1,4,3,2] => [.,[[[.,.],.],.]] => 0
[2,1,3,4] => [[.,.],[.,[.,.]]] => 0
[2,1,4,3] => [[.,.],[[.,.],.]] => 0
[2,3,1,4] => [[.,.],[.,[.,.]]] => 0
[2,3,4,1] => [[.,.],[.,[.,.]]] => 0
[2,4,1,3] => [[.,.],[[.,.],.]] => 0
[2,4,3,1] => [[.,.],[[.,.],.]] => 0
[3,1,2,4] => [[.,[.,.]],[.,.]] => 0
[3,1,4,2] => [[.,[.,.]],[.,.]] => 0
[3,2,1,4] => [[[.,.],.],[.,.]] => 0
[3,2,4,1] => [[[.,.],.],[.,.]] => 0
[3,4,1,2] => [[.,[.,.]],[.,.]] => 0
[3,4,2,1] => [[[.,.],.],[.,.]] => 0
[4,1,2,3] => [[.,[.,[.,.]]],.] => 0
[4,1,3,2] => [[.,[[.,.],.]],.] => 0
[4,2,1,3] => [[[.,.],[.,.]],.] => 0
[4,2,3,1] => [[[.,.],[.,.]],.] => 0
[4,3,1,2] => [[[.,[.,.]],.],.] => 0
[4,3,2,1] => [[[[.,.],.],.],.] => 0
[1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 0
[1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 0
[1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 0
[1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]] => 0
[1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]] => 1
[1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => 0
[1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 0
[1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => 0
[1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]] => 0
[1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]] => 0
[1,3,5,2,4] => [.,[[.,.],[[.,.],.]]] => 0
[1,3,5,4,2] => [.,[[.,.],[[.,.],.]]] => 0
[1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]] => 0
[1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]] => 0
[1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => 0
[1,4,3,5,2] => [.,[[[.,.],.],[.,.]]] => 0
[1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => 0
[1,4,5,3,2] => [.,[[[.,.],.],[.,.]]] => 0
[1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]] => 0
[1,5,2,4,3] => [.,[[.,[[.,.],.]],.]] => 0
[1,5,3,2,4] => [.,[[[.,.],[.,.]],.]] => 0
[1,5,3,4,2] => [.,[[[.,.],[.,.]],.]] => 0
[1,5,4,2,3] => [.,[[[.,[.,.]],.],.]] => 0
[1,5,4,3,2] => [.,[[[[.,.],.],.],.]] => 0
[2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => 0
[2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => 0
[2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => 0
[2,1,4,5,3] => [[.,.],[[.,.],[.,.]]] => 0
[2,1,5,3,4] => [[.,.],[[.,[.,.]],.]] => 0
[2,1,5,4,3] => [[.,.],[[[.,.],.],.]] => 0
[2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]] => 0
[2,3,1,5,4] => [[.,.],[.,[[.,.],.]]] => 0
[2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]] => 0
[2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]] => 0
[2,3,5,1,4] => [[.,.],[.,[[.,.],.]]] => 0
[2,3,5,4,1] => [[.,.],[.,[[.,.],.]]] => 0
[2,4,1,3,5] => [[.,.],[[.,.],[.,.]]] => 0
[2,4,1,5,3] => [[.,.],[[.,.],[.,.]]] => 0
[2,4,3,1,5] => [[.,.],[[.,.],[.,.]]] => 0
[2,4,3,5,1] => [[.,.],[[.,.],[.,.]]] => 0
[2,4,5,1,3] => [[.,.],[[.,.],[.,.]]] => 0
[2,4,5,3,1] => [[.,.],[[.,.],[.,.]]] => 0
[2,5,1,3,4] => [[.,.],[[.,[.,.]],.]] => 0
[2,5,1,4,3] => [[.,.],[[[.,.],.],.]] => 0
[2,5,3,1,4] => [[.,.],[[.,[.,.]],.]] => 0
[2,5,3,4,1] => [[.,.],[[.,[.,.]],.]] => 0
[2,5,4,1,3] => [[.,.],[[[.,.],.],.]] => 0
[2,5,4,3,1] => [[.,.],[[[.,.],.],.]] => 0
[3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]] => 0
[3,1,2,5,4] => [[.,[.,.]],[[.,.],.]] => 0
[3,1,4,2,5] => [[.,[.,.]],[.,[.,.]]] => 0
[3,1,4,5,2] => [[.,[.,.]],[.,[.,.]]] => 0
[3,1,5,2,4] => [[.,[.,.]],[[.,.],.]] => 0
[3,1,5,4,2] => [[.,[.,.]],[[.,.],.]] => 0
[3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => 0
[3,2,1,5,4] => [[[.,.],.],[[.,.],.]] => 0
[3,2,4,1,5] => [[[.,.],.],[.,[.,.]]] => 0
[3,2,4,5,1] => [[[.,.],.],[.,[.,.]]] => 0
[3,2,5,1,4] => [[[.,.],.],[[.,.],.]] => 0
[3,2,5,4,1] => [[[.,.],.],[[.,.],.]] => 0
[3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => 0
[3,4,1,5,2] => [[.,[.,.]],[.,[.,.]]] => 0
[3,4,2,1,5] => [[[.,.],.],[.,[.,.]]] => 0
[3,4,2,5,1] => [[[.,.],.],[.,[.,.]]] => 0
[3,4,5,1,2] => [[.,[.,.]],[.,[.,.]]] => 0
[3,4,5,2,1] => [[[.,.],.],[.,[.,.]]] => 0
[3,5,1,2,4] => [[.,[.,.]],[[.,.],.]] => 0
[3,5,1,4,2] => [[.,[.,.]],[[.,.],.]] => 0
>>> Load all 5913 entries. <<<[3,5,2,1,4] => [[[.,.],.],[[.,.],.]] => 0
[3,5,2,4,1] => [[[.,.],.],[[.,.],.]] => 0
[3,5,4,1,2] => [[.,[.,.]],[[.,.],.]] => 0
[3,5,4,2,1] => [[[.,.],.],[[.,.],.]] => 0
[4,1,2,3,5] => [[.,[.,[.,.]]],[.,.]] => 0
[4,1,2,5,3] => [[.,[.,[.,.]]],[.,.]] => 0
[4,1,3,2,5] => [[.,[[.,.],.]],[.,.]] => 0
[4,1,3,5,2] => [[.,[[.,.],.]],[.,.]] => 0
[4,1,5,2,3] => [[.,[.,[.,.]]],[.,.]] => 0
[4,1,5,3,2] => [[.,[[.,.],.]],[.,.]] => 0
[4,2,1,3,5] => [[[.,.],[.,.]],[.,.]] => 0
[4,2,1,5,3] => [[[.,.],[.,.]],[.,.]] => 0
[4,2,3,1,5] => [[[.,.],[.,.]],[.,.]] => 0
[4,2,3,5,1] => [[[.,.],[.,.]],[.,.]] => 0
[4,2,5,1,3] => [[[.,.],[.,.]],[.,.]] => 0
[4,2,5,3,1] => [[[.,.],[.,.]],[.,.]] => 0
[4,3,1,2,5] => [[[.,[.,.]],.],[.,.]] => 0
[4,3,1,5,2] => [[[.,[.,.]],.],[.,.]] => 0
[4,3,2,1,5] => [[[[.,.],.],.],[.,.]] => 0
[4,3,2,5,1] => [[[[.,.],.],.],[.,.]] => 0
[4,3,5,1,2] => [[[.,[.,.]],.],[.,.]] => 0
[4,3,5,2,1] => [[[[.,.],.],.],[.,.]] => 0
[4,5,1,2,3] => [[.,[.,[.,.]]],[.,.]] => 0
[4,5,1,3,2] => [[.,[[.,.],.]],[.,.]] => 0
[4,5,2,1,3] => [[[.,.],[.,.]],[.,.]] => 0
[4,5,2,3,1] => [[[.,.],[.,.]],[.,.]] => 0
[4,5,3,1,2] => [[[.,[.,.]],.],[.,.]] => 0
[4,5,3,2,1] => [[[[.,.],.],.],[.,.]] => 0
[5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.] => 0
[5,1,2,4,3] => [[.,[.,[[.,.],.]]],.] => 0
[5,1,3,2,4] => [[.,[[.,.],[.,.]]],.] => 0
[5,1,3,4,2] => [[.,[[.,.],[.,.]]],.] => 0
[5,1,4,2,3] => [[.,[[.,[.,.]],.]],.] => 0
[5,1,4,3,2] => [[.,[[[.,.],.],.]],.] => 0
[5,2,1,3,4] => [[[.,.],[.,[.,.]]],.] => 0
[5,2,1,4,3] => [[[.,.],[[.,.],.]],.] => 0
[5,2,3,1,4] => [[[.,.],[.,[.,.]]],.] => 0
[5,2,3,4,1] => [[[.,.],[.,[.,.]]],.] => 0
[5,2,4,1,3] => [[[.,.],[[.,.],.]],.] => 0
[5,2,4,3,1] => [[[.,.],[[.,.],.]],.] => 0
[5,3,1,2,4] => [[[.,[.,.]],[.,.]],.] => 0
[5,3,1,4,2] => [[[.,[.,.]],[.,.]],.] => 0
[5,3,2,1,4] => [[[[.,.],.],[.,.]],.] => 0
[5,3,2,4,1] => [[[[.,.],.],[.,.]],.] => 0
[5,3,4,1,2] => [[[.,[.,.]],[.,.]],.] => 0
[5,3,4,2,1] => [[[[.,.],.],[.,.]],.] => 0
[5,4,1,2,3] => [[[.,[.,[.,.]]],.],.] => 0
[5,4,1,3,2] => [[[.,[[.,.],.]],.],.] => 0
[5,4,2,1,3] => [[[[.,.],[.,.]],.],.] => 0
[5,4,2,3,1] => [[[[.,.],[.,.]],.],.] => 0
[5,4,3,1,2] => [[[[.,[.,.]],.],.],.] => 0
[5,4,3,2,1] => [[[[[.,.],.],.],.],.] => 0
[1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
[1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 0
[1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 0
[1,2,3,5,6,4] => [.,[.,[.,[[.,.],[.,.]]]]] => 0
[1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]] => 1
[1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]] => 0
[1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 0
[1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => 0
[1,2,4,5,3,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 0
[1,2,4,5,6,3] => [.,[.,[[.,.],[.,[.,.]]]]] => 0
[1,2,4,6,3,5] => [.,[.,[[.,.],[[.,.],.]]]] => 0
[1,2,4,6,5,3] => [.,[.,[[.,.],[[.,.],.]]]] => 0
[1,2,5,3,4,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[1,2,5,3,6,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]] => 0
[1,2,5,4,6,3] => [.,[.,[[[.,.],.],[.,.]]]] => 0
[1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 1
[1,2,5,6,4,3] => [.,[.,[[[.,.],.],[.,.]]]] => 0
[1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]] => 1
[1,2,6,3,5,4] => [.,[.,[[.,[[.,.],.]],.]]] => 1
[1,2,6,4,3,5] => [.,[.,[[[.,.],[.,.]],.]]] => 1
[1,2,6,4,5,3] => [.,[.,[[[.,.],[.,.]],.]]] => 1
[1,2,6,5,3,4] => [.,[.,[[[.,[.,.]],.],.]]] => 0
[1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]] => 0
[1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 0
[1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 0
[1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => 0
[1,3,2,5,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => 0
[1,3,2,6,4,5] => [.,[[.,.],[[.,[.,.]],.]]] => 1
[1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]] => 0
[1,3,4,2,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 0
[1,3,4,2,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 0
[1,3,4,5,2,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 0
[1,3,4,5,6,2] => [.,[[.,.],[.,[.,[.,.]]]]] => 0
[1,3,4,6,2,5] => [.,[[.,.],[.,[[.,.],.]]]] => 0
[1,3,4,6,5,2] => [.,[[.,.],[.,[[.,.],.]]]] => 0
[1,3,5,2,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => 0
[1,3,5,2,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => 0
[1,3,5,4,2,6] => [.,[[.,.],[[.,.],[.,.]]]] => 0
[1,3,5,4,6,2] => [.,[[.,.],[[.,.],[.,.]]]] => 0
[1,3,5,6,2,4] => [.,[[.,.],[[.,.],[.,.]]]] => 0
[1,3,5,6,4,2] => [.,[[.,.],[[.,.],[.,.]]]] => 0
[1,3,6,2,4,5] => [.,[[.,.],[[.,[.,.]],.]]] => 1
[1,3,6,2,5,4] => [.,[[.,.],[[[.,.],.],.]]] => 0
[1,3,6,4,2,5] => [.,[[.,.],[[.,[.,.]],.]]] => 1
[1,3,6,4,5,2] => [.,[[.,.],[[.,[.,.]],.]]] => 1
[1,3,6,5,2,4] => [.,[[.,.],[[[.,.],.],.]]] => 0
[1,3,6,5,4,2] => [.,[[.,.],[[[.,.],.],.]]] => 0
[1,4,2,3,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 0
[1,4,2,3,6,5] => [.,[[.,[.,.]],[[.,.],.]]] => 0
[1,4,2,5,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 0
[1,4,2,5,6,3] => [.,[[.,[.,.]],[.,[.,.]]]] => 0
[1,4,2,6,3,5] => [.,[[.,[.,.]],[[.,.],.]]] => 0
[1,4,2,6,5,3] => [.,[[.,[.,.]],[[.,.],.]]] => 0
[1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]] => 0
[1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]] => 0
[1,4,3,5,2,6] => [.,[[[.,.],.],[.,[.,.]]]] => 0
[1,4,3,5,6,2] => [.,[[[.,.],.],[.,[.,.]]]] => 0
[1,4,3,6,2,5] => [.,[[[.,.],.],[[.,.],.]]] => 0
[1,4,3,6,5,2] => [.,[[[.,.],.],[[.,.],.]]] => 0
[1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 0
[1,4,5,2,6,3] => [.,[[.,[.,.]],[.,[.,.]]]] => 0
[1,4,5,3,2,6] => [.,[[[.,.],.],[.,[.,.]]]] => 0
[1,4,5,3,6,2] => [.,[[[.,.],.],[.,[.,.]]]] => 0
[1,4,5,6,2,3] => [.,[[.,[.,.]],[.,[.,.]]]] => 0
[1,4,5,6,3,2] => [.,[[[.,.],.],[.,[.,.]]]] => 0
[1,4,6,2,3,5] => [.,[[.,[.,.]],[[.,.],.]]] => 0
[1,4,6,2,5,3] => [.,[[.,[.,.]],[[.,.],.]]] => 0
[1,4,6,3,2,5] => [.,[[[.,.],.],[[.,.],.]]] => 0
[1,4,6,3,5,2] => [.,[[[.,.],.],[[.,.],.]]] => 0
[1,4,6,5,2,3] => [.,[[.,[.,.]],[[.,.],.]]] => 0
[1,4,6,5,3,2] => [.,[[[.,.],.],[[.,.],.]]] => 0
[1,5,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,.]]] => 0
[1,5,2,3,6,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 0
[1,5,2,4,3,6] => [.,[[.,[[.,.],.]],[.,.]]] => 0
[1,5,2,4,6,3] => [.,[[.,[[.,.],.]],[.,.]]] => 0
[1,5,2,6,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 0
[1,5,2,6,4,3] => [.,[[.,[[.,.],.]],[.,.]]] => 0
[1,5,3,2,4,6] => [.,[[[.,.],[.,.]],[.,.]]] => 0
[1,5,3,2,6,4] => [.,[[[.,.],[.,.]],[.,.]]] => 0
[1,5,3,4,2,6] => [.,[[[.,.],[.,.]],[.,.]]] => 0
[1,5,3,4,6,2] => [.,[[[.,.],[.,.]],[.,.]]] => 0
[1,5,3,6,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => 0
[1,5,3,6,4,2] => [.,[[[.,.],[.,.]],[.,.]]] => 0
[1,5,4,2,3,6] => [.,[[[.,[.,.]],.],[.,.]]] => 0
[1,5,4,2,6,3] => [.,[[[.,[.,.]],.],[.,.]]] => 0
[1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]] => 0
[1,5,4,3,6,2] => [.,[[[[.,.],.],.],[.,.]]] => 0
[1,5,4,6,2,3] => [.,[[[.,[.,.]],.],[.,.]]] => 0
[1,5,4,6,3,2] => [.,[[[[.,.],.],.],[.,.]]] => 0
[1,5,6,2,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 0
[1,5,6,2,4,3] => [.,[[.,[[.,.],.]],[.,.]]] => 0
[1,5,6,3,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => 0
[1,5,6,3,4,2] => [.,[[[.,.],[.,.]],[.,.]]] => 0
[1,5,6,4,2,3] => [.,[[[.,[.,.]],.],[.,.]]] => 0
[1,5,6,4,3,2] => [.,[[[[.,.],.],.],[.,.]]] => 0
[1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]] => 0
[1,6,2,3,5,4] => [.,[[.,[.,[[.,.],.]]],.]] => 0
[1,6,2,4,3,5] => [.,[[.,[[.,.],[.,.]]],.]] => 0
[1,6,2,4,5,3] => [.,[[.,[[.,.],[.,.]]],.]] => 0
[1,6,2,5,3,4] => [.,[[.,[[.,[.,.]],.]],.]] => 0
[1,6,2,5,4,3] => [.,[[.,[[[.,.],.],.]],.]] => 0
[1,6,3,2,4,5] => [.,[[[.,.],[.,[.,.]]],.]] => 0
[1,6,3,2,5,4] => [.,[[[.,.],[[.,.],.]],.]] => 0
[1,6,3,4,2,5] => [.,[[[.,.],[.,[.,.]]],.]] => 0
[1,6,3,4,5,2] => [.,[[[.,.],[.,[.,.]]],.]] => 0
[1,6,3,5,2,4] => [.,[[[.,.],[[.,.],.]],.]] => 0
[1,6,3,5,4,2] => [.,[[[.,.],[[.,.],.]],.]] => 0
[1,6,4,2,3,5] => [.,[[[.,[.,.]],[.,.]],.]] => 0
[1,6,4,2,5,3] => [.,[[[.,[.,.]],[.,.]],.]] => 0
[1,6,4,3,2,5] => [.,[[[[.,.],.],[.,.]],.]] => 0
[1,6,4,3,5,2] => [.,[[[[.,.],.],[.,.]],.]] => 0
[1,6,4,5,2,3] => [.,[[[.,[.,.]],[.,.]],.]] => 0
[1,6,4,5,3,2] => [.,[[[[.,.],.],[.,.]],.]] => 0
[1,6,5,2,3,4] => [.,[[[.,[.,[.,.]]],.],.]] => 0
[1,6,5,2,4,3] => [.,[[[.,[[.,.],.]],.],.]] => 0
[1,6,5,3,2,4] => [.,[[[[.,.],[.,.]],.],.]] => 0
[1,6,5,3,4,2] => [.,[[[[.,.],[.,.]],.],.]] => 0
[1,6,5,4,2,3] => [.,[[[[.,[.,.]],.],.],.]] => 0
[1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]] => 0
[2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 0
[2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => 0
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[7,6,5,1,2,3,4] => [[[[.,[.,[.,[.,.]]]],.],.],.] => 0
[7,6,5,1,2,4,3] => [[[[.,[.,[[.,.],.]]],.],.],.] => 0
[7,6,5,1,3,2,4] => [[[[.,[[.,.],[.,.]]],.],.],.] => 0
[7,6,5,1,3,4,2] => [[[[.,[[.,.],[.,.]]],.],.],.] => 0
[7,6,5,1,4,2,3] => [[[[.,[[.,[.,.]],.]],.],.],.] => 0
[7,6,5,1,4,3,2] => [[[[.,[[[.,.],.],.]],.],.],.] => 0
[7,6,5,2,1,3,4] => [[[[[.,.],[.,[.,.]]],.],.],.] => 0
[7,6,5,2,1,4,3] => [[[[[.,.],[[.,.],.]],.],.],.] => 0
[7,6,5,2,3,1,4] => [[[[[.,.],[.,[.,.]]],.],.],.] => 0
[7,6,5,2,3,4,1] => [[[[[.,.],[.,[.,.]]],.],.],.] => 0
[7,6,5,2,4,1,3] => [[[[[.,.],[[.,.],.]],.],.],.] => 0
[7,6,5,2,4,3,1] => [[[[[.,.],[[.,.],.]],.],.],.] => 0
[7,6,5,3,1,2,4] => [[[[[.,[.,.]],[.,.]],.],.],.] => 0
[7,6,5,3,1,4,2] => [[[[[.,[.,.]],[.,.]],.],.],.] => 0
[7,6,5,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],.] => 0
[7,6,5,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],.],.] => 0
[7,6,5,3,4,1,2] => [[[[[.,[.,.]],[.,.]],.],.],.] => 0
[7,6,5,3,4,2,1] => [[[[[[.,.],.],[.,.]],.],.],.] => 0
[7,6,5,4,1,2,3] => [[[[[.,[.,[.,.]]],.],.],.],.] => 0
[7,6,5,4,1,3,2] => [[[[[.,[[.,.],.]],.],.],.],.] => 0
[7,6,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],.] => 0
[7,6,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],.],.] => 0
[7,6,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],.] => 0
[7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.] => 0
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Generating function
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Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
119,1 702,18 4795,245
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 6$
$F_{4} = 24$
$F_{5} = 119 + q$
$F_{6} = 702 + 18\ q$
$F_{7} = 4795 + 245\ q$
Description
The number of occurrences of the contiguous pattern [.,[.,[[.,[.,.]],.]]] in a binary tree.
oeis:A159769 counts binary trees avoiding this pattern.
oeis:A159769 counts binary trees avoiding this pattern.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
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