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Identifier

Mp00103: Dyck paths —peeling map⟶ Dyck paths

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 2325 entries. <<<

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Description

Send a Dyck path to its peeled Dyck path.

References

[1] Stump, C. More bijective Catalan combinatorics on permutations and on signed permutations MathSciNet:3153083

Properties

graded

Sage code

def mapping(D):
    n = D.semilength()
    area = D.to_area_sequence()
    new_area = []
    touch_sequences = []
    touches = []
    for i in range(n-1):
        if area[i+1] == 0:
            touches.append(i+1)
            if len(touches) > 1:
                touch_sequences.append(touches)
                touches = []
            elif area[i] == 0:
                touches = []
            new_area.append(0)
        elif area[i+1] == 1:
            new_area.append(0)
            touches.append(i+1)
        else:
            new_area.append(area[i+1]-2)
    new_area.append(0)
    if area[n - 1] != 0:
        touches.append(n)
        if len(touches) > 1:
            touch_sequences.append(touches)
    return DyckWords().from_area_sequence(new_area)

Weight

Created

Jan 29, 2020 at 13:25 by FindStatCrew

Updated

May 11, 2021 at 15:01 by Martin Rubey