- FindStat

Identifier

St001214: Integer partitions ⟶ ℤ

Values

=>
                            Cc0002;cc-rep
                            
                            
                            

                        []=>0
[1]=>0
[2]=>0
[1,1]=>0
[3]=>0
[2,1]=>1
[1,1,1]=>0
[4]=>0
[3,1]=>1
[2,2]=>2
[2,1,1]=>1
[1,1,1,1]=>0
[5]=>0
[4,1]=>1
[3,2]=>2
[3,1,1]=>2
[2,2,1]=>2
[2,1,1,1]=>1
[1,1,1,1,1]=>0
[6]=>0
[5,1]=>1
[4,2]=>2
[4,1,1]=>2
[3,3]=>3
[3,2,1]=>3
[3,1,1,1]=>2
[2,2,2]=>3
[2,2,1,1]=>2
[2,1,1,1,1]=>1
[1,1,1,1,1,1]=>0
[7]=>0
[6,1]=>1
[5,2]=>2
[5,1,1]=>2
[4,3]=>3
[4,2,1]=>3
[4,1,1,1]=>3
[3,3,1]=>4
[3,2,2]=>4
[3,2,1,1]=>3
[3,1,1,1,1]=>2
[2,2,2,1]=>3
[2,2,1,1,1]=>2
[2,1,1,1,1,1]=>1
[1,1,1,1,1,1,1]=>0
[8]=>0
[7,1]=>1
[6,2]=>2
[6,1,1]=>2
[5,3]=>3
[5,2,1]=>3
[5,1,1,1]=>3
[4,4]=>4
[4,3,1]=>4
[4,2,2]=>4
[4,2,1,1]=>4
[4,1,1,1,1]=>3
[3,3,2]=>5
[3,3,1,1]=>4
[3,2,2,1]=>4
[3,2,1,1,1]=>3
[3,1,1,1,1,1]=>2
[2,2,2,2]=>4
[2,2,2,1,1]=>3
[2,2,1,1,1,1]=>2
[2,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1]=>0
[9]=>0
[8,1]=>1
[7,2]=>2
[7,1,1]=>2
[6,3]=>3
[6,2,1]=>3
[6,1,1,1]=>3
[5,4]=>4
[5,3,1]=>4
[5,2,2]=>4
[5,2,1,1]=>4
[5,1,1,1,1]=>4
[4,4,1]=>5
[4,3,2]=>5
[4,3,1,1]=>5
[4,2,2,1]=>5
[4,2,1,1,1]=>4
[4,1,1,1,1,1]=>3
[3,3,3]=>6
[3,3,2,1]=>5
[3,3,1,1,1]=>4
[3,2,2,2]=>5
[3,2,2,1,1]=>4
[3,2,1,1,1,1]=>3
[3,1,1,1,1,1,1]=>2
[2,2,2,2,1]=>4
[2,2,2,1,1,1]=>3
[2,2,1,1,1,1,1]=>2
[2,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1]=>0
[10]=>0
[9,1]=>1
[8,2]=>2
[8,1,1]=>2
[7,3]=>3
[7,2,1]=>3
[7,1,1,1]=>3
[6,4]=>4
[6,3,1]=>4
[6,2,2]=>4
[6,2,1,1]=>4
[6,1,1,1,1]=>4
[5,5]=>5
[5,4,1]=>5
[5,3,2]=>5
[5,3,1,1]=>5
[5,2,2,1]=>5
[5,2,1,1,1]=>5
[5,1,1,1,1,1]=>4
[4,4,2]=>6
[4,4,1,1]=>6
[4,3,3]=>6
[4,3,2,1]=>6
[4,3,1,1,1]=>5
[4,2,2,2]=>6
[4,2,2,1,1]=>5
[4,2,1,1,1,1]=>4
[4,1,1,1,1,1,1]=>3
[3,3,3,1]=>6
[3,3,2,2]=>6
[3,3,2,1,1]=>5
[3,3,1,1,1,1]=>4
[3,2,2,2,1]=>5
[3,2,2,1,1,1]=>4
[3,2,1,1,1,1,1]=>3
[3,1,1,1,1,1,1,1]=>2
[2,2,2,2,2]=>5
[2,2,2,2,1,1]=>4
[2,2,2,1,1,1,1]=>3
[2,2,1,1,1,1,1,1]=>2
[2,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1,1]=>0
[5,4,2]=>6
[5,4,1,1]=>6
[5,3,3]=>6
[5,3,2,1]=>6
[5,3,1,1,1]=>6
[5,2,2,2]=>6
[5,2,2,1,1]=>6
[4,4,3]=>7
[4,4,2,1]=>7
[4,4,1,1,1]=>6
[4,3,3,1]=>7
[4,3,2,2]=>7
[4,3,2,1,1]=>6
[4,2,2,2,1]=>6
[3,3,3,2]=>7
[3,3,3,1,1]=>6
[3,3,2,2,1]=>6
[6,4,2]=>6
[5,4,3]=>7
[5,4,2,1]=>7
[5,4,1,1,1]=>7
[5,3,3,1]=>7
[5,3,2,2]=>7
[5,3,2,1,1]=>7
[5,2,2,2,1]=>7
[4,4,3,1]=>8
[4,4,2,2]=>8
[4,4,2,1,1]=>7
[4,3,3,2]=>8
[4,3,3,1,1]=>7
[4,3,2,2,1]=>7
[3,3,3,2,1]=>7
[3,3,2,2,1,1]=>6
[5,4,3,1]=>8
[5,4,2,2]=>8
[5,4,2,1,1]=>8
[5,3,3,2]=>8
[5,3,3,1,1]=>8
[5,3,2,2,1]=>8
[4,4,3,2]=>9
[4,4,3,1,1]=>8
[4,4,2,2,1]=>8
[4,3,3,2,1]=>8
[5,4,3,2]=>9
[5,4,3,1,1]=>9
[5,4,2,2,1]=>9
[5,3,3,2,1]=>9
[4,4,3,2,1]=>9
[5,4,3,2,1]=>10
                    

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 aft of an integer partition.
The aft is the size of the partition minus the length of the first row or column, whichever is larger.
See also St000784The maximum of the length and the largest part of the integer partition..

Code

def statistic(L):
    if L:
        return sum(L)-max(L[0],len(L))
    else:
        return 0

Created

Jun 21, 2018 at 00:45 by Sara Billey

Updated

Jan 22, 2023 at 11:54 by Martin Rubey