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Identifier

Mp00102: Dyck paths —rise composition⟶ Integer compositions

Images

[] => []

[1,0] => [1]

[1,0,1,0] => [1,1]

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

[1,0,1,0,1,0] => [1,1,1]

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

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

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

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

[1,0,1,0,1,0,1,0] => [1,1,1,1]

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 6302 entries. <<<

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

Description

Send a Dyck path to the composition of sizes of its rises.

Properties

surjective, graded

Sage code

def mapping(D):
    return D.rise_composition()

Weight

Created

Jan 29, 2020 at 13:25 by FindStatCrew

Updated

Apr 04, 2022 at 13:54 by Tilman Möller