- FindStat

Identifier

St000380: Integer partitions ⟶ ℤ

Values

[] => 0

[1] => 2

[2] => 3

[1,1] => 3

[3] => 4

[2,1] => 3

[1,1,1] => 4

[4] => 5

[3,1] => 4

[2,2] => 4

[2,1,1] => 4

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

[5] => 6

[4,1] => 5

[3,2] => 4

[3,1,1] => 4

[2,2,1] => 4

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

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

[6] => 7

[5,1] => 6

[4,2] => 5

[4,1,1] => 5

[3,3] => 5

[3,2,1] => 4

[3,1,1,1] => 5

[2,2,2] => 5

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

[2,1,1,1,1] => 6

[1,1,1,1,1,1] => 7

[7] => 8

[6,1] => 7

[5,2] => 6

[5,1,1] => 6

[4,3] => 5

[4,2,1] => 5

[4,1,1,1] => 5

[3,3,1] => 5

[3,2,2] => 5

[3,2,1,1] => 5

[3,1,1,1,1] => 6

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

[2,2,1,1,1] => 6

[2,1,1,1,1,1] => 7

[1,1,1,1,1,1,1] => 8

[8] => 9

[7,1] => 8

[6,2] => 7

[6,1,1] => 7

[5,3] => 6

[5,2,1] => 6

[5,1,1,1] => 6

[4,4] => 6

[4,3,1] => 5

[4,2,2] => 5

[4,2,1,1] => 5

[4,1,1,1,1] => 6

[3,3,2] => 5

[3,3,1,1] => 5

[3,2,2,1] => 5

[3,2,1,1,1] => 6

[3,1,1,1,1,1] => 7

[2,2,2,2] => 6

[2,2,2,1,1] => 6

[2,2,1,1,1,1] => 7

[2,1,1,1,1,1,1] => 8

[1,1,1,1,1,1,1,1] => 9

[9] => 10

[8,1] => 9

[7,2] => 8

[7,1,1] => 8

[6,3] => 7

[6,2,1] => 7

[6,1,1,1] => 7

[5,4] => 6

[5,3,1] => 6

[5,2,2] => 6

[5,2,1,1] => 6

[5,1,1,1,1] => 6

[4,4,1] => 6

[4,3,2] => 5

[4,3,1,1] => 5

[4,2,2,1] => 5

[4,2,1,1,1] => 6

[4,1,1,1,1,1] => 7

[3,3,3] => 6

[3,3,2,1] => 5

[3,3,1,1,1] => 6

[3,2,2,2] => 6

[3,2,2,1,1] => 6

[3,2,1,1,1,1] => 7

[3,1,1,1,1,1,1] => 8

[2,2,2,2,1] => 6

[2,2,2,1,1,1] => 7

[2,2,1,1,1,1,1] => 8

[2,1,1,1,1,1,1,1] => 9

[1,1,1,1,1,1,1,1,1] => 10

[10] => 11

[9,1] => 10

[8,2] => 9

[8,1,1] => 9

>>> Load all 360 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

Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition.
Put differently, this is the smallest number $n$ such that the partition fits into the triangular partition $(n-1,n-2,\dots,1)$.

Code

def statistic(p):
    if p:
        return max( p[i]+i+1 for i in range(len(p)) )
    return 0

Created

Feb 09, 2016 at 12:26 by Christian Stump

Updated

Feb 25, 2021 at 20:07 by Martin Rubey