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Identifier

Mp00180: Integer compositions —to ribbon⟶ Skew partitions

Images

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

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

[2] => [[2],[]]

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

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

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

[3] => [[3],[]]

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

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

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

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

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

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

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

[4] => [[4],[]]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[5] => [[5],[]]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[6] => [[6],[]]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,6] => [[6,1],[]]

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

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

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

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

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

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

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Description

The ribbon shape corresponding to an integer composition.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.

Properties

injective, graded

Sage code

def mapping(a):
    return a.to_skew_partition()

Weight

Created

Sep 22, 2020 at 11:07 by Martin Rubey

Updated

Sep 22, 2020 at 11:07 by Martin Rubey