- FindStat

Identifier

Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 2507 entries. <<<

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

first fundamental transformation

Description

Return the permutation whose cycles are the subsequences between successive left to right maxima.

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.