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Identifier

Mp00072: Permutations —binary search tree: left to right⟶ Binary trees

Images

[] => .

[1] => [.,.]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]

[1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]

[1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]

[1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]]

[1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]]

[1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]

[1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]

[1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]

[1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]]

[1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]]

[1,3,5,2,4] => [.,[[.,.],[[.,.],.]]]

[1,3,5,4,2] => [.,[[.,.],[[.,.],.]]]

[1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]]

[1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]]

[1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]

[1,4,3,5,2] => [.,[[[.,.],.],[.,.]]]

[1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]

[1,4,5,3,2] => [.,[[[.,.],.],[.,.]]]

[1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]

[1,5,2,4,3] => [.,[[.,[[.,.],.]],.]]

[1,5,3,2,4] => [.,[[[.,.],[.,.]],.]]

[1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]

[1,5,4,2,3] => [.,[[[.,[.,.]],.],.]]

[1,5,4,3,2] => [.,[[[[.,.],.],.],.]]

[2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]

[2,1,3,5,4] => [[.,.],[.,[[.,.],.]]]

[2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]

[2,1,4,5,3] => [[.,.],[[.,.],[.,.]]]

[2,1,5,3,4] => [[.,.],[[.,[.,.]],.]]

[2,1,5,4,3] => [[.,.],[[[.,.],.],.]]

[2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]]

[2,3,1,5,4] => [[.,.],[.,[[.,.],.]]]

[2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]]

[2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]]

[2,3,5,1,4] => [[.,.],[.,[[.,.],.]]]

[2,3,5,4,1] => [[.,.],[.,[[.,.],.]]]

[2,4,1,3,5] => [[.,.],[[.,.],[.,.]]]

[2,4,1,5,3] => [[.,.],[[.,.],[.,.]]]

[2,4,3,1,5] => [[.,.],[[.,.],[.,.]]]

[2,4,3,5,1] => [[.,.],[[.,.],[.,.]]]

[2,4,5,1,3] => [[.,.],[[.,.],[.,.]]]

[2,4,5,3,1] => [[.,.],[[.,.],[.,.]]]

[2,5,1,3,4] => [[.,.],[[.,[.,.]],.]]

[2,5,1,4,3] => [[.,.],[[[.,.],.],.]]

[2,5,3,1,4] => [[.,.],[[.,[.,.]],.]]

[2,5,3,4,1] => [[.,.],[[.,[.,.]],.]]

[2,5,4,1,3] => [[.,.],[[[.,.],.],.]]

[2,5,4,3,1] => [[.,.],[[[.,.],.],.]]

[3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]]

[3,1,2,5,4] => [[.,[.,.]],[[.,.],.]]

[3,1,4,2,5] => [[.,[.,.]],[.,[.,.]]]

[3,1,4,5,2] => [[.,[.,.]],[.,[.,.]]]

[3,1,5,2,4] => [[.,[.,.]],[[.,.],.]]

[3,1,5,4,2] => [[.,[.,.]],[[.,.],.]]

[3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]

[3,2,1,5,4] => [[[.,.],.],[[.,.],.]]

[3,2,4,1,5] => [[[.,.],.],[.,[.,.]]]

[3,2,4,5,1] => [[[.,.],.],[.,[.,.]]]

[3,2,5,1,4] => [[[.,.],.],[[.,.],.]]

[3,2,5,4,1] => [[[.,.],.],[[.,.],.]]

[3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]]

[3,4,1,5,2] => [[.,[.,.]],[.,[.,.]]]

[3,4,2,1,5] => [[[.,.],.],[.,[.,.]]]

[3,4,2,5,1] => [[[.,.],.],[.,[.,.]]]

[3,4,5,1,2] => [[.,[.,.]],[.,[.,.]]]

[3,4,5,2,1] => [[[.,.],.],[.,[.,.]]]

[3,5,1,2,4] => [[.,[.,.]],[[.,.],.]]

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click to show experimental identities (only identities of compositions of up to three maps are shown)

Description

Return the shape of the binary search tree of the permutation as a non labelled binary tree.

Properties

surjective, graded

Sage code

def mapping(elt):
    return elt.binary_search_tree(left_to_right=True).shape()

Weight

Created

Jan 26, 2020 at 12:32 by FindStatCrew

Updated

Jan 26, 2020 at 12:32 by Martin Rubey