Identifier
Values
=>
Cc0002;cc-rep
[]=>0
[1]=>1
[2]=>2
[1,1]=>2
[3]=>3
[2,1]=>2
[1,1,1]=>3
[4]=>4
[3,1]=>3
[2,2]=>2
[2,1,1]=>3
[1,1,1,1]=>4
[5]=>5
[4,1]=>4
[3,2]=>3
[3,1,1]=>3
[2,2,1]=>3
[2,1,1,1]=>4
[1,1,1,1,1]=>5
[6]=>6
[5,1]=>5
[4,2]=>4
[4,1,1]=>4
[3,3]=>3
[3,2,1]=>3
[3,1,1,1]=>4
[2,2,2]=>3
[2,2,1,1]=>4
[2,1,1,1,1]=>5
[1,1,1,1,1,1]=>6
[7]=>7
[6,1]=>6
[5,2]=>5
[5,1,1]=>5
[4,3]=>4
[4,2,1]=>4
[4,1,1,1]=>4
[3,3,1]=>3
[3,2,2]=>3
[3,2,1,1]=>4
[3,1,1,1,1]=>5
[2,2,2,1]=>4
[2,2,1,1,1]=>5
[2,1,1,1,1,1]=>6
[1,1,1,1,1,1,1]=>7
[8]=>8
[7,1]=>7
[6,2]=>6
[6,1,1]=>6
[5,3]=>5
[5,2,1]=>5
[5,1,1,1]=>5
[4,4]=>4
[4,3,1]=>4
[4,2,2]=>4
[4,2,1,1]=>4
[4,1,1,1,1]=>5
[3,3,2]=>3
[3,3,1,1]=>4
[3,2,2,1]=>4
[3,2,1,1,1]=>5
[3,1,1,1,1,1]=>6
[2,2,2,2]=>4
[2,2,2,1,1]=>5
[2,2,1,1,1,1]=>6
[2,1,1,1,1,1,1]=>7
[1,1,1,1,1,1,1,1]=>8
[9]=>9
[8,1]=>8
[7,2]=>7
[7,1,1]=>7
[6,3]=>6
[6,2,1]=>6
[6,1,1,1]=>6
[5,4]=>5
[5,3,1]=>5
[5,2,2]=>5
[5,2,1,1]=>5
[5,1,1,1,1]=>5
[4,4,1]=>4
[4,3,2]=>4
[4,3,1,1]=>4
[4,2,2,1]=>4
[4,2,1,1,1]=>5
[4,1,1,1,1,1]=>6
[3,3,3]=>3
[3,3,2,1]=>4
[3,3,1,1,1]=>5
[3,2,2,2]=>4
[3,2,2,1,1]=>5
[3,2,1,1,1,1]=>6
[3,1,1,1,1,1,1]=>7
[2,2,2,2,1]=>5
[2,2,2,1,1,1]=>6
[2,2,1,1,1,1,1]=>7
[2,1,1,1,1,1,1,1]=>8
[1,1,1,1,1,1,1,1,1]=>9
[10]=>10
[9,1]=>9
[8,2]=>8
[8,1,1]=>8
[7,3]=>7
[7,2,1]=>7
[7,1,1,1]=>7
[6,4]=>6
[6,3,1]=>6
[6,2,2]=>6
[6,2,1,1]=>6
[6,1,1,1,1]=>6
[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]=>6
[4,4,2]=>4
[4,4,1,1]=>4
[4,3,3]=>4
[4,3,2,1]=>4
[4,3,1,1,1]=>5
[4,2,2,2]=>4
[4,2,2,1,1]=>5
[4,2,1,1,1,1]=>6
[4,1,1,1,1,1,1]=>7
[3,3,3,1]=>4
[3,3,2,2]=>4
[3,3,2,1,1]=>5
[3,3,1,1,1,1]=>6
[3,2,2,2,1]=>5
[3,2,2,1,1,1]=>6
[3,2,1,1,1,1,1]=>7
[3,1,1,1,1,1,1,1]=>8
[2,2,2,2,2]=>5
[2,2,2,2,1,1]=>6
[2,2,2,1,1,1,1]=>7
[2,2,1,1,1,1,1,1]=>8
[2,1,1,1,1,1,1,1,1]=>9
[1,1,1,1,1,1,1,1,1,1]=>10
[11]=>11
[10,1]=>10
[9,2]=>9
[9,1,1]=>9
[8,3]=>8
[8,2,1]=>8
[8,1,1,1]=>8
[7,4]=>7
[7,3,1]=>7
[7,2,2]=>7
[7,2,1,1]=>7
[7,1,1,1,1]=>7
[6,5]=>6
[6,4,1]=>6
[6,3,2]=>6
[6,3,1,1]=>6
[6,2,2,1]=>6
[6,2,1,1,1]=>6
[6,1,1,1,1,1]=>6
[5,5,1]=>5
[5,4,2]=>5
[5,4,1,1]=>5
[5,3,3]=>5
[5,3,2,1]=>5
[5,3,1,1,1]=>5
[5,2,2,2]=>5
[5,2,2,1,1]=>5
[5,2,1,1,1,1]=>6
[5,1,1,1,1,1,1]=>7
[4,4,3]=>4
[4,4,2,1]=>4
[4,4,1,1,1]=>5
[4,3,3,1]=>4
[4,3,2,2]=>4
[4,3,2,1,1]=>5
[4,3,1,1,1,1]=>6
[4,2,2,2,1]=>5
[4,2,2,1,1,1]=>6
[4,2,1,1,1,1,1]=>7
[4,1,1,1,1,1,1,1]=>8
[3,3,3,2]=>4
[3,3,3,1,1]=>5
[3,3,2,2,1]=>5
[3,3,2,1,1,1]=>6
[3,3,1,1,1,1,1]=>7
[3,2,2,2,2]=>5
[3,2,2,2,1,1]=>6
[3,2,2,1,1,1,1]=>7
[3,2,1,1,1,1,1,1]=>8
[3,1,1,1,1,1,1,1,1]=>9
[2,2,2,2,2,1]=>6
[2,2,2,2,1,1,1]=>7
[2,2,2,1,1,1,1,1]=>8
[2,2,1,1,1,1,1,1,1]=>9
[2,1,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,1,1,1,1,1,1,1]=>11
[12]=>12
[11,1]=>11
[10,2]=>10
[10,1,1]=>10
[9,3]=>9
[9,2,1]=>9
[9,1,1,1]=>9
[8,4]=>8
[8,3,1]=>8
[8,2,2]=>8
[8,2,1,1]=>8
[8,1,1,1,1]=>8
[7,5]=>7
[7,4,1]=>7
[7,3,2]=>7
[7,3,1,1]=>7
[7,2,2,1]=>7
[7,2,1,1,1]=>7
[7,1,1,1,1,1]=>7
[6,6]=>6
[6,5,1]=>6
[6,4,2]=>6
[6,4,1,1]=>6
[6,3,3]=>6
[6,3,2,1]=>6
[6,3,1,1,1]=>6
[6,2,2,2]=>6
[6,2,2,1,1]=>6
[6,2,1,1,1,1]=>6
[6,1,1,1,1,1,1]=>7
[5,5,2]=>5
[5,5,1,1]=>5
[5,4,3]=>5
[5,4,2,1]=>5
[5,4,1,1,1]=>5
[5,3,3,1]=>5
[5,3,2,2]=>5
[5,3,2,1,1]=>5
[5,3,1,1,1,1]=>6
[5,2,2,2,1]=>5
[5,2,2,1,1,1]=>6
[5,2,1,1,1,1,1]=>7
[5,1,1,1,1,1,1,1]=>8
[4,4,4]=>4
[4,4,3,1]=>4
[4,4,2,2]=>4
[4,4,2,1,1]=>5
[4,4,1,1,1,1]=>6
[4,3,3,2]=>4
[4,3,3,1,1]=>5
[4,3,2,2,1]=>5
[4,3,2,1,1,1]=>6
[4,3,1,1,1,1,1]=>7
[4,2,2,2,2]=>5
[4,2,2,2,1,1]=>6
[4,2,2,1,1,1,1]=>7
[4,2,1,1,1,1,1,1]=>8
[4,1,1,1,1,1,1,1,1]=>9
[3,3,3,3]=>4
[3,3,3,2,1]=>5
[3,3,3,1,1,1]=>6
[3,3,2,2,2]=>5
[3,3,2,2,1,1]=>6
[3,3,2,1,1,1,1]=>7
[3,3,1,1,1,1,1,1]=>8
[3,2,2,2,2,1]=>6
[3,2,2,2,1,1,1]=>7
[3,2,2,1,1,1,1,1]=>8
[3,2,1,1,1,1,1,1,1]=>9
[3,1,1,1,1,1,1,1,1,1]=>10
[2,2,2,2,2,2]=>6
[2,2,2,2,2,1,1]=>7
[2,2,2,2,1,1,1,1]=>8
[2,2,2,1,1,1,1,1,1]=>9
[2,2,1,1,1,1,1,1,1,1]=>10
[2,1,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,1,1,1,1,1,1,1,1]=>12
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
Description
The maximum of the length and the largest part of the integer partition.
This is the side length of the smallest square the Ferrers diagram of the partition fits into. It is also the minimal number of colours required to colour the cells of the Ferrers diagram such that no two cells in a column or in a row have the same colour, see [1].
See also St001214The aft of an integer partition..
This is the side length of the smallest square the Ferrers diagram of the partition fits into. It is also the minimal number of colours required to colour the cells of the Ferrers diagram such that no two cells in a column or in a row have the same colour, see [1].
See also St001214The aft of an integer partition..
References
[1] Chow, T. Coloring a Ferrers diagram MathOverflow:203962
Code
def statistic(pi):
if pi:
return max(pi[0], len(pi))
return 0
Created
Apr 19, 2017 at 09:45 by Martin Rubey
Updated
Jan 22, 2023 at 11:56 by Martin Rubey
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!