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]=>3
[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]=>4
[3,2,1]=>3
[3,1,1,1]=>4
[2,2,2]=>4
[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]=>4
[3,2,2]=>4
[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]=>5
[4,3,1]=>4
[4,2,2]=>4
[4,2,1,1]=>4
[4,1,1,1,1]=>5
[3,3,2]=>4
[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]=>5
[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]=>5
[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]=>5
[3,3,2,1]=>4
[3,3,1,1,1]=>5
[3,2,2,2]=>5
[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]=>6
[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]=>5
[4,4,1,1]=>5
[4,3,3]=>5
[4,3,2,1]=>4
[4,3,1,1,1]=>5
[4,2,2,2]=>5
[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]=>5
[3,3,2,2]=>5
[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]=>6
[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]=>6
[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]=>5
[4,4,2,1]=>5
[4,4,1,1,1]=>5
[4,3,3,1]=>5
[4,3,2,2]=>5
[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]=>5
[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]=>6
[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]=>7
[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]=>6
[5,5,1,1]=>6
[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]=>6
[4,4,3,1]=>5
[4,4,2,2]=>5
[4,4,2,1,1]=>5
[4,4,1,1,1,1]=>6
[4,3,3,2]=>5
[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]=>6
[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]=>6
[3,3,3,2,1]=>5
[3,3,3,1,1,1]=>6
[3,3,2,2,2]=>6
[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]=>7
[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
[5,4,3,1]=>5
[5,4,2,2]=>5
[5,4,2,1,1]=>5
[5,3,3,2]=>5
[5,3,3,1,1]=>5
[5,3,2,2,1]=>5
[4,4,3,2]=>5
[4,4,3,1,1]=>5
[4,4,2,2,1]=>5
[4,3,3,2,1]=>5
[5,4,3,2]=>5
[5,4,3,1,1]=>5
[5,4,2,2,1]=>5
[5,3,3,2,1]=>5
[4,4,3,2,1]=>5
[5,4,3,2,1]=>5
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Description
The maximal part of the shifted composition of an integer partition.
A partition $\lambda = (\lambda_1,\ldots,\lambda_k)$ is shifted into a composition by adding $i-1$ to the $i$-th part.
The statistic is then $\operatorname{max}_i\{ \lambda_i + i - 1 \}$.
See also St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition..
A partition $\lambda = (\lambda_1,\ldots,\lambda_k)$ is shifted into a composition by adding $i-1$ to the $i$-th part.
The statistic is then $\operatorname{max}_i\{ \lambda_i + i - 1 \}$.
See also St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition..
Code
def statistic(p):
if len(p) == 0:
return 0
return max( p[i]+i for i in range(len(p)) )
Created
Feb 09, 2016 at 12:23 by Christian Stump
Updated
May 24, 2018 at 13:24 by Martin Rubey
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