- FindStat

edit this statistic or download as text // json

Identifier

St000748: Set partitions ⟶ ℤ

Values

{{1,2}} => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

{{1,2,3,4,5}} => 0

{{1,2,3,4},{5}} => 0

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

{{1,2,3},{4,5}} => 0

{{1,2,3},{4},{5}} => 0

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

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

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

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

{{1,2},{3,4,5}} => 0

{{1,2},{3,4},{5}} => 0

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

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

{{1,2},{3},{4,5}} => 0

{{1,2},{3},{4},{5}} => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

{{1},{2,3,4,5}} => 0

{{1},{2,3,4},{5}} => 0

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

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

{{1},{2,3},{4,5}} => 0

{{1},{2,3},{4},{5}} => 0

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

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

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

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

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

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

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

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

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

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

{{1},{2},{3,4,5}} => 0

{{1},{2},{3,4},{5}} => 0

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

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

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

{{1},{2},{3},{4,5}} => 0

{{1},{2},{3},{4},{5}} => 0

{{1,2,3,4,5,6}} => 0

{{1,2,3,4,5},{6}} => 0

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

{{1,2,3,4},{5,6}} => 0

{{1,2,3,4},{5},{6}} => 0

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

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

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

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

{{1,2,3},{4,5,6}} => 0

{{1,2,3},{4,5},{6}} => 0

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

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

{{1,2,3},{4},{5,6}} => 0

{{1,2,3},{4},{5},{6}} => 0

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

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

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

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

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

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

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

{{1,2,4},{3,6},{5}} => 8

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

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

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

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

>>> Load all 1200 entries. <<<

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

Description

The major index of the permutation obtained by flattening the set partition.
A set partition can be represented by a sequence of blocks where the first entries of the blocks and the blocks themselves are increasing. This statistic is then the major index of the permutation obtained by flattening the set partition in this canonical form.

Code

def statistic(SP):
    SP = sorted( sorted(B) for B in SP )
    pi = sum(SP,[])
    alpha = [ len(B) for B in SP ]
    return sum( i+1 for i in range(len(pi)-1) if pi[i] > pi[i+1] )

Created

Apr 04, 2017 at 17:27 by Christian Stump

Updated

Apr 04, 2017 at 17:27 by Christian Stump