- FindStat

Identifier

St000473: Integer partitions ⟶ ℤ

Values

[] => 0

[1] => 0

[2] => 1

[1,1] => 0

[3] => 1

[2,1] => 1

[1,1,1] => 0

[4] => 1

[3,1] => 1

[2,2] => 2

[2,1,1] => 0

[1,1,1,1] => 0

[5] => 1

[4,1] => 1

[3,2] => 2

[3,1,1] => 1

[2,2,1] => 2

[2,1,1,1] => 0

[1,1,1,1,1] => 0

[6] => 1

[5,1] => 1

[4,2] => 2

[4,1,1] => 1

[3,3] => 2

[3,2,1] => 2

[3,1,1,1] => 0

[2,2,2] => 3

[2,2,1,1] => 0

[2,1,1,1,1] => 0

[1,1,1,1,1,1] => 0

[7] => 1

[6,1] => 1

[5,2] => 2

[5,1,1] => 1

[4,3] => 2

[4,2,1] => 2

[4,1,1,1] => 1

[3,3,1] => 2

[3,2,2] => 3

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

[3,1,1,1,1] => 0

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

[2,2,1,1,1] => 0

[2,1,1,1,1,1] => 0

[1,1,1,1,1,1,1] => 0

[8] => 1

[7,1] => 1

[6,2] => 2

[6,1,1] => 1

[5,3] => 2

[5,2,1] => 2

[5,1,1,1] => 1

[4,4] => 2

[4,3,1] => 2

[4,2,2] => 3

[4,2,1,1] => 1

[4,1,1,1,1] => 0

[3,3,2] => 3

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

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

[3,2,1,1,1] => 0

[3,1,1,1,1,1] => 0

[2,2,2,2] => 4

[2,2,2,1,1] => 0

[2,2,1,1,1,1] => 0

[2,1,1,1,1,1,1] => 0

[1,1,1,1,1,1,1,1] => 0

[9] => 1

[8,1] => 1

[7,2] => 2

[7,1,1] => 1

[6,3] => 2

[6,2,1] => 2

[6,1,1,1] => 1

[5,4] => 2

[5,3,1] => 2

[5,2,2] => 3

[5,2,1,1] => 1

[5,1,1,1,1] => 1

[4,4,1] => 2

[4,3,2] => 3

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

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

[4,2,1,1,1] => 1

[4,1,1,1,1,1] => 0

[3,3,3] => 3

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

[3,3,1,1,1] => 0

[3,2,2,2] => 4

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

[3,2,1,1,1,1] => 0

[3,1,1,1,1,1,1] => 0

[2,2,2,2,1] => 4

[2,2,2,1,1,1] => 0

[2,2,1,1,1,1,1] => 0

[2,1,1,1,1,1,1,1] => 0

[1,1,1,1,1,1,1,1,1] => 0

[10] => 1

[9,1] => 1

[8,2] => 2

[8,1,1] => 1

>>> Load all 272 entries. <<<

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Description

The number of parts of a partition that are strictly bigger than the number of ones.
This is part of the definition of Dyson's crank of a partition, see St000474Dyson's crank of a partition..

References

[1] Andrews, G. E., Garvan, F. G. Dyson's crank of a partition MathSciNet:0929094

Code

def statistic(L):
    ones = list(L).count(1)
    return sum(1 for part in L if part > ones)

Created

Apr 19, 2016 at 10:40 by Christian Stump

Updated

Oct 29, 2017 at 21:13 by Martin Rubey