- FindStat

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Identifier

Mp00079: Set partitions —shape⟶ Integer partitions

Images

{{1}} => [1]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

{{1,2,3,4,5,6}} => [6]

{{1,2,3,4,5},{6}} => [5,1]

{{1,2,3,4,6},{5}} => [5,1]

{{1,2,3,4},{5,6}} => [4,2]

{{1,2,3,4},{5},{6}} => [4,1,1]

{{1,2,3,5,6},{4}} => [5,1]

{{1,2,3,5},{4,6}} => [4,2]

{{1,2,3,5},{4},{6}} => [4,1,1]

{{1,2,3,6},{4,5}} => [4,2]

{{1,2,3},{4,5,6}} => [3,3]

{{1,2,3},{4,5},{6}} => [3,2,1]

{{1,2,3,6},{4},{5}} => [4,1,1]

{{1,2,3},{4,6},{5}} => [3,2,1]

{{1,2,3},{4},{5,6}} => [3,2,1]

{{1,2,3},{4},{5},{6}} => [3,1,1,1]

{{1,2,4,5,6},{3}} => [5,1]

{{1,2,4,5},{3,6}} => [4,2]

{{1,2,4,5},{3},{6}} => [4,1,1]

{{1,2,4,6},{3,5}} => [4,2]

{{1,2,4},{3,5,6}} => [3,3]

{{1,2,4},{3,5},{6}} => [3,2,1]

{{1,2,4,6},{3},{5}} => [4,1,1]

{{1,2,4},{3,6},{5}} => [3,2,1]

{{1,2,4},{3},{5,6}} => [3,2,1]

{{1,2,4},{3},{5},{6}} => [3,1,1,1]

{{1,2,5,6},{3,4}} => [4,2]

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Description

Sends a set partition to the integer partition obtained by the sizes of the blocks.

Properties

surjective, graded

Sage code

def mapping(elt):
    return elt.shape()

Weight

Created

Jan 26, 2020 at 12:32 by FindStatCrew

Updated

Jan 26, 2020 at 12:32 by Martin Rubey