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Identifier

Mp00286: Ordered set partitions —to permutation⟶ Permutations

Images

[{1}] => [1]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

Return the permutation obtained by concatenating the blocks sorted into increasing order.

Properties

surjective, graded

Sage code

def mapping(pi):
    return Permutation([e for b in pi for e in sorted(b)])

Weight

Created

May 24, 2023 at 17:06 by Martin Rubey

Updated

May 24, 2023 at 17:06 by Martin Rubey