Identifier
Values
=>
Cc0002;cc-rep
[]=>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
[7,3]=>8
[7,2,1]=>8
[7,1,1,1]=>8
[6,4]=>7
[6,3,1]=>7
[6,2,2]=>7
[6,2,1,1]=>7
[6,1,1,1,1]=>7
[5,5]=>7
[5,4,1]=>6
[5,3,2]=>6
[5,3,1,1]=>6
[5,2,2,1]=>6
[5,2,1,1,1]=>6
[5,1,1,1,1,1]=>7
[4,4,2]=>6
[4,4,1,1]=>6
[4,3,3]=>6
[4,3,2,1]=>5
[4,3,1,1,1]=>6
[4,2,2,2]=>6
[4,2,2,1,1]=>6
[4,2,1,1,1,1]=>7
[4,1,1,1,1,1,1]=>8
[3,3,3,1]=>6
[3,3,2,2]=>6
[3,3,2,1,1]=>6
[3,3,1,1,1,1]=>7
[3,2,2,2,1]=>6
[3,2,2,1,1,1]=>7
[3,2,1,1,1,1,1]=>8
[3,1,1,1,1,1,1,1]=>9
[2,2,2,2,2]=>7
[2,2,2,2,1,1]=>7
[2,2,2,1,1,1,1]=>8
[2,2,1,1,1,1,1,1]=>9
[2,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,1,1,1,1,1,1]=>11
[11]=>12
[10,1]=>11
[9,2]=>10
[9,1,1]=>10
[8,3]=>9
[8,2,1]=>9
[8,1,1,1]=>9
[7,4]=>8
[7,3,1]=>8
[7,2,2]=>8
[7,2,1,1]=>8
[7,1,1,1,1]=>8
[6,5]=>7
[6,4,1]=>7
[6,3,2]=>7
[6,3,1,1]=>7
[6,2,2,1]=>7
[6,2,1,1,1]=>7
[6,1,1,1,1,1]=>7
[5,5,1]=>7
[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
[5,2,1,1,1,1]=>7
[5,1,1,1,1,1,1]=>8
[4,4,3]=>6
[4,4,2,1]=>6
[4,4,1,1,1]=>6
[4,3,3,1]=>6
[4,3,2,2]=>6
[4,3,2,1,1]=>6
[4,3,1,1,1,1]=>7
[4,2,2,2,1]=>6
[4,2,2,1,1,1]=>7
[4,2,1,1,1,1,1]=>8
[4,1,1,1,1,1,1,1]=>9
[3,3,3,2]=>6
[3,3,3,1,1]=>6
[3,3,2,2,1]=>6
[3,3,2,1,1,1]=>7
[3,3,1,1,1,1,1]=>8
[3,2,2,2,2]=>7
[3,2,2,2,1,1]=>7
[3,2,2,1,1,1,1]=>8
[3,2,1,1,1,1,1,1]=>9
[3,1,1,1,1,1,1,1,1]=>10
[2,2,2,2,2,1]=>7
[2,2,2,2,1,1,1]=>8
[2,2,2,1,1,1,1,1]=>9
[2,2,1,1,1,1,1,1,1]=>10
[2,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,1,1,1,1,1,1,1]=>12
[12]=>13
[11,1]=>12
[10,2]=>11
[10,1,1]=>11
[9,3]=>10
[9,2,1]=>10
[9,1,1,1]=>10
[8,4]=>9
[8,3,1]=>9
[8,2,2]=>9
[8,2,1,1]=>9
[8,1,1,1,1]=>9
[7,5]=>8
[7,4,1]=>8
[7,3,2]=>8
[7,3,1,1]=>8
[7,2,2,1]=>8
[7,2,1,1,1]=>8
[7,1,1,1,1,1]=>8
[6,6]=>8
[6,5,1]=>7
[6,4,2]=>7
[6,4,1,1]=>7
[6,3,3]=>7
[6,3,2,1]=>7
[6,3,1,1,1]=>7
[6,2,2,2]=>7
[6,2,2,1,1]=>7
[6,2,1,1,1,1]=>7
[6,1,1,1,1,1,1]=>8
[5,5,2]=>7
[5,5,1,1]=>7
[5,4,3]=>6
[5,4,2,1]=>6
[5,4,1,1,1]=>6
[5,3,3,1]=>6
[5,3,2,2]=>6
[5,3,2,1,1]=>6
[5,3,1,1,1,1]=>7
[5,2,2,2,1]=>6
[5,2,2,1,1,1]=>7
[5,2,1,1,1,1,1]=>8
[5,1,1,1,1,1,1,1]=>9
[4,4,4]=>7
[4,4,3,1]=>6
[4,4,2,2]=>6
[4,4,2,1,1]=>6
[4,4,1,1,1,1]=>7
[4,3,3,2]=>6
[4,3,3,1,1]=>6
[4,3,2,2,1]=>6
[4,3,2,1,1,1]=>7
[4,3,1,1,1,1,1]=>8
[4,2,2,2,2]=>7
[4,2,2,2,1,1]=>7
[4,2,2,1,1,1,1]=>8
[4,2,1,1,1,1,1,1]=>9
[4,1,1,1,1,1,1,1,1]=>10
[3,3,3,3]=>7
[3,3,3,2,1]=>6
[3,3,3,1,1,1]=>7
[3,3,2,2,2]=>7
[3,3,2,2,1,1]=>7
[3,3,2,1,1,1,1]=>8
[3,3,1,1,1,1,1,1]=>9
[3,2,2,2,2,1]=>7
[3,2,2,2,1,1,1]=>8
[3,2,2,1,1,1,1,1]=>9
[3,2,1,1,1,1,1,1,1]=>10
[3,1,1,1,1,1,1,1,1,1]=>11
[2,2,2,2,2,2]=>8
[2,2,2,2,2,1,1]=>8
[2,2,2,2,1,1,1,1]=>9
[2,2,2,1,1,1,1,1,1]=>10
[2,2,1,1,1,1,1,1,1,1]=>11
[2,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,1,1,1,1,1,1,1,1]=>13
[8,5]=>9
[7,5,1]=>8
[7,4,2]=>8
[5,5,3]=>7
[5,4,4]=>7
[5,4,3,1]=>6
[5,4,2,2]=>6
[5,4,2,1,1]=>6
[5,3,3,2]=>6
[5,3,3,1,1]=>6
[5,3,2,2,1]=>6
[4,4,4,1]=>7
[4,4,3,2]=>6
[4,4,3,1,1]=>6
[4,4,2,2,1]=>6
[4,3,3,3]=>7
[4,3,3,2,1]=>6
[3,3,3,3,1]=>7
[3,3,3,2,2]=>7
[9,5]=>10
[8,5,1]=>9
[7,5,2]=>8
[7,4,3]=>8
[5,5,4]=>7
[5,4,3,2]=>6
[5,4,3,1,1]=>6
[5,4,2,2,1]=>6
[5,3,3,2,1]=>6
[5,3,2,2,2]=>7
[4,4,4,2]=>7
[4,4,3,3]=>7
[4,4,3,2,1]=>6
[3,3,3,3,2]=>7
[9,5,1]=>10
[8,5,2]=>9
[7,5,3]=>8
[5,5,5]=>8
[5,4,3,2,1]=>6
[5,3,2,2,2,1]=>7
[4,4,4,3]=>7
[3,3,3,3,3]=>8
[8,5,3]=>9
[7,5,3,1]=>8
[4,4,4,4]=>8
[8,6,3]=>9
[9,6,3]=>10
[8,6,4]=>9
[9,6,4]=>10
[8,5,4,2]=>9
[8,5,5,1]=>9
[7,5,4,3,1]=>8
[8,6,4,2]=>9
[10,6,4]=>11
[10,7,3]=>11
[9,7,4]=>10
[9,5,5,1]=>10
[6,5,4,3,2,1]=>7
[11,7,3]=>12
[9,6,4,3]=>10
[9,6,5,3]=>10
[8,6,5,3,1]=>9
[11,7,5,1]=>12
[9,7,5,3]=>10
[9,7,5,3,1]=>10
[10,7,5,3]=>11
[9,7,5,4,1]=>10
[7,6,5,4,3,2,1]=>8
[10,7,6,4,1]=>11
[9,7,6,4,2]=>10
[10,8,5,4,1]=>11
[10,8,6,4,1]=>11
[9,7,5,5,3,1]=>10
[11,8,6,4,1]=>12
[10,8,6,4,2]=>11
[11,8,6,5,1]=>12
[12,9,7,5,1]=>13
[13,9,7,5,1]=>14
[11,9,7,5,3,1]=>12
[11,8,7,5,4,1]=>12
[8,7,6,5,4,3,2,1]=>9
[11,9,7,5,5,3]=>12
[11,9,7,7,5,3,3]=>12
[11,9,7,6,5,3,1]=>12
[13,11,9,7,5,3,1]=>14
[13,11,9,7,7,5,3,1]=>14
[17,13,11,9,7,5,1]=>18
[15,13,11,9,7,5,3,1]=>16
[29,23,19,17,13,11,7,1]=>30
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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 $(n-1,n-2,\dots,1)$.
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
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