- FindStat

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Identifier

St000249: Set partitions ⟶ ℤ

Values

{{1,2}} => 2

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

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

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

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

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

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

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

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

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

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

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

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

{{1,3},{2,4}} => 0

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

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

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

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

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

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

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

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

{{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}} => 4

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

{{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}} => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The number of singletons (St000247The number of singleton blocks of a set partition.) plus the number of antisingletons (St000248The number of anti-singletons of a set partition.) of a set partition.

References

[1] Birdsong, S., Hetyei, Gábor The Toric h-Vector of a Cubical Complex in Terms of Noncrossing Partition Statistics DOI:10.1007/s00026-014-0243-8

Code

def statistic(S):
    n = S.size()
    return sum( 1 for B in S for i in B if (i%n)+1 in B ) + sum( 1 for B in S if len(B) == 1 )

Created

May 05, 2015 at 11:04 by Christian Stump

Updated

Jun 01, 2015 at 17:53 by Martin Rubey