- FindStat

Identifier

Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
St000132: Binary trees ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,4]] => [1,2] => [.,[.,.]] => 0

[[2,4]] => [1,2] => [.,[.,.]] => 0

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

[[4,4]] => [1,2] => [.,[.,.]] => 0

[[1],[4]] => [2,1] => [[.,.],.] => 0

[[2],[4]] => [2,1] => [[.,.],.] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,5]] => [1,2] => [.,[.,.]] => 0

[[2,5]] => [1,2] => [.,[.,.]] => 0

[[3,5]] => [1,2] => [.,[.,.]] => 0

[[4,5]] => [1,2] => [.,[.,.]] => 0

[[5,5]] => [1,2] => [.,[.,.]] => 0

[[1],[5]] => [2,1] => [[.,.],.] => 0

[[2],[5]] => [2,1] => [[.,.],.] => 0

[[3],[5]] => [2,1] => [[.,.],.] => 0

[[4],[5]] => [2,1] => [[.,.],.] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The number of occurrences of the contiguous pattern [[.,.],[.,[[.,.],.]]] in a binary tree.
oeis:A159773 counts binary trees avoiding this pattern.

Map

reading word permutation

Description

Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottommost row (in English notation).

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.