- FindStat

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Identifier

Mp00290: Parking functions —to ordered set partition⟶ Ordered set partitions

Images

[1] => [{1}]

[1,1] => [{1,2}]

[1,2] => [{1},{2}]

[2,1] => [{2},{1}]

[1,1,1] => [{1,2,3}]

[1,1,2] => [{1,2},{3}]

[1,2,1] => [{1,3},{2}]

[2,1,1] => [{2,3},{1}]

[1,1,3] => [{1,2},{3}]

[1,3,1] => [{1,3},{2}]

[3,1,1] => [{2,3},{1}]

[1,2,2] => [{1},{2,3}]

[2,1,2] => [{2},{1,3}]

[2,2,1] => [{3},{1,2}]

[1,2,3] => [{1},{2},{3}]

[1,3,2] => [{1},{3},{2}]

[2,1,3] => [{2},{1},{3}]

[2,3,1] => [{3},{1},{2}]

[3,1,2] => [{2},{3},{1}]

[3,2,1] => [{3},{2},{1}]

[1,1,1,1] => [{1,2,3,4}]

[1,1,1,2] => [{1,2,3},{4}]

[1,1,2,1] => [{1,2,4},{3}]

[1,2,1,1] => [{1,3,4},{2}]

[2,1,1,1] => [{2,3,4},{1}]

[1,1,1,3] => [{1,2,3},{4}]

[1,1,3,1] => [{1,2,4},{3}]

[1,3,1,1] => [{1,3,4},{2}]

[3,1,1,1] => [{2,3,4},{1}]

[1,1,1,4] => [{1,2,3},{4}]

[1,1,4,1] => [{1,2,4},{3}]

[1,4,1,1] => [{1,3,4},{2}]

[4,1,1,1] => [{2,3,4},{1}]

[1,1,2,2] => [{1,2},{3,4}]

[1,2,1,2] => [{1,3},{2,4}]

[1,2,2,1] => [{1,4},{2,3}]

[2,1,1,2] => [{2,3},{1,4}]

[2,1,2,1] => [{2,4},{1,3}]

[2,2,1,1] => [{3,4},{1,2}]

[1,1,2,3] => [{1,2},{3},{4}]

[1,1,3,2] => [{1,2},{4},{3}]

[1,2,1,3] => [{1,3},{2},{4}]

[1,2,3,1] => [{1,4},{2},{3}]

[1,3,1,2] => [{1,3},{4},{2}]

[1,3,2,1] => [{1,4},{3},{2}]

[2,1,1,3] => [{2,3},{1},{4}]

[2,1,3,1] => [{2,4},{1},{3}]

[2,3,1,1] => [{3,4},{1},{2}]

[3,1,1,2] => [{2,3},{4},{1}]

[3,1,2,1] => [{2,4},{3},{1}]

[3,2,1,1] => [{3,4},{2},{1}]

[1,1,2,4] => [{1,2},{3},{4}]

[1,1,4,2] => [{1,2},{4},{3}]

[1,2,1,4] => [{1,3},{2},{4}]

[1,2,4,1] => [{1,4},{2},{3}]

[1,4,1,2] => [{1,3},{4},{2}]

[1,4,2,1] => [{1,4},{3},{2}]

[2,1,1,4] => [{2,3},{1},{4}]

[2,1,4,1] => [{2,4},{1},{3}]

[2,4,1,1] => [{3,4},{1},{2}]

[4,1,1,2] => [{2,3},{4},{1}]

[4,1,2,1] => [{2,4},{3},{1}]

[4,2,1,1] => [{3,4},{2},{1}]

[1,1,3,3] => [{1,2},{3,4}]

[1,3,1,3] => [{1,3},{2,4}]

[1,3,3,1] => [{1,4},{2,3}]

[3,1,1,3] => [{2,3},{1,4}]

[3,1,3,1] => [{2,4},{1,3}]

[3,3,1,1] => [{3,4},{1,2}]

[1,1,3,4] => [{1,2},{3},{4}]

[1,1,4,3] => [{1,2},{4},{3}]

[1,3,1,4] => [{1,3},{2},{4}]

[1,3,4,1] => [{1,4},{2},{3}]

[1,4,1,3] => [{1,3},{4},{2}]

[1,4,3,1] => [{1,4},{3},{2}]

[3,1,1,4] => [{2,3},{1},{4}]

[3,1,4,1] => [{2,4},{1},{3}]

[3,4,1,1] => [{3,4},{1},{2}]

[4,1,1,3] => [{2,3},{4},{1}]

[4,1,3,1] => [{2,4},{3},{1}]

[4,3,1,1] => [{3,4},{2},{1}]

[1,2,2,2] => [{1},{2,3,4}]

[2,1,2,2] => [{2},{1,3,4}]

[2,2,1,2] => [{3},{1,2,4}]

[2,2,2,1] => [{4},{1,2,3}]

[1,2,2,3] => [{1},{2,3},{4}]

[1,2,3,2] => [{1},{2,4},{3}]

[1,3,2,2] => [{1},{3,4},{2}]

[2,1,2,3] => [{2},{1,3},{4}]

[2,1,3,2] => [{2},{1,4},{3}]

[2,2,1,3] => [{3},{1,2},{4}]

[2,2,3,1] => [{4},{1,2},{3}]

[2,3,1,2] => [{3},{1,4},{2}]

[2,3,2,1] => [{4},{1,3},{2}]

[3,1,2,2] => [{2},{3,4},{1}]

[3,2,1,2] => [{3},{2,4},{1}]

[3,2,2,1] => [{4},{2,3},{1}]

[1,2,2,4] => [{1},{2,3},{4}]

[1,2,4,2] => [{1},{2,4},{3}]

[1,4,2,2] => [{1},{3,4},{2}]

[2,1,2,4] => [{2},{1,3},{4}]

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Description

Return the ordered set partition whose blocks are the labels of the runs of the labelled Dyck path.

Properties

surjective, graded

Sage code

def mapping(p):
    w = p.to_labelled_dyck_word()
    pi = []
    b = []
    for e in w:
        if e:
            b.append(e)
        elif b:
            pi.append(b)
            b = []
    return OrderedSetPartition(pi)

Weight

Created

May 24, 2023 at 17:25 by Martin Rubey

Updated

May 24, 2023 at 17:25 by Martin Rubey