- FindStat

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Identifier

St000971: Set partitions ⟶ ℤ

Values

{{1}} => 1

{{1,2}} => 2

{{1},{2}} => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The smallest closer of a set partition.
A closer (or right hand endpoint) of a set partition is a number that is maximal in its block. For this statistic, singletons are considered as closers.
In other words, this is the smallest among the maximal elements of the blocks.

References

[1] Tichenor, T. A note on graph compositions and their connection to minimax of set partitions arXiv:1709.00393

Code

def statistic(S):
    return min(max(b) for b in S)

Created

Sep 04, 2017 at 06:51 by Martin Rubey

Updated

Apr 03, 2018 at 21:01 by Martin Rubey