Identifier
Identifier
Values
[] generating graphics... => 0
[1] generating graphics... => 1
[2] generating graphics... => 2
[1,1] generating graphics... => 2
[3] generating graphics... => 3
[2,1] generating graphics... => 2
[1,1,1] generating graphics... => 3
[4] generating graphics... => 4
[3,1] generating graphics... => 3
[2,2] generating graphics... => 3
[2,1,1] generating graphics... => 3
[1,1,1,1] generating graphics... => 4
[5] generating graphics... => 5
[4,1] generating graphics... => 4
[3,2] generating graphics... => 3
[3,1,1] generating graphics... => 3
[2,2,1] generating graphics... => 3
[2,1,1,1] generating graphics... => 4
[1,1,1,1,1] generating graphics... => 5
[6] generating graphics... => 6
[5,1] generating graphics... => 5
[4,2] generating graphics... => 4
[4,1,1] generating graphics... => 4
[3,3] generating graphics... => 4
[3,2,1] generating graphics... => 3
[3,1,1,1] generating graphics... => 4
[2,2,2] generating graphics... => 4
[2,2,1,1] generating graphics... => 4
[2,1,1,1,1] generating graphics... => 5
[1,1,1,1,1,1] generating graphics... => 6
[7] generating graphics... => 7
[6,1] generating graphics... => 6
[5,2] generating graphics... => 5
[5,1,1] generating graphics... => 5
[4,3] generating graphics... => 4
[4,2,1] generating graphics... => 4
[4,1,1,1] generating graphics... => 4
[3,3,1] generating graphics... => 4
[3,2,2] generating graphics... => 4
[3,2,1,1] generating graphics... => 4
[3,1,1,1,1] generating graphics... => 5
[2,2,2,1] generating graphics... => 4
[2,2,1,1,1] generating graphics... => 5
[2,1,1,1,1,1] generating graphics... => 6
[1,1,1,1,1,1,1] generating graphics... => 7
[8] generating graphics... => 8
[7,1] generating graphics... => 7
[6,2] generating graphics... => 6
[6,1,1] generating graphics... => 6
[5,3] generating graphics... => 5
[5,2,1] generating graphics... => 5
[5,1,1,1] generating graphics... => 5
[4,4] generating graphics... => 5
[4,3,1] generating graphics... => 4
[4,2,2] generating graphics... => 4
[4,2,1,1] generating graphics... => 4
[4,1,1,1,1] generating graphics... => 5
[3,3,2] generating graphics... => 4
[3,3,1,1] generating graphics... => 4
[3,2,2,1] generating graphics... => 4
[3,2,1,1,1] generating graphics... => 5
[3,1,1,1,1,1] generating graphics... => 6
[2,2,2,2] generating graphics... => 5
[2,2,2,1,1] generating graphics... => 5
[2,2,1,1,1,1] generating graphics... => 6
[2,1,1,1,1,1,1] generating graphics... => 7
[1,1,1,1,1,1,1,1] generating graphics... => 8
[9] generating graphics... => 9
[8,1] generating graphics... => 8
[7,2] generating graphics... => 7
[7,1,1] generating graphics... => 7
[6,3] generating graphics... => 6
[6,2,1] generating graphics... => 6
[6,1,1,1] generating graphics... => 6
[5,4] generating graphics... => 5
[5,3,1] generating graphics... => 5
[5,2,2] generating graphics... => 5
[5,2,1,1] generating graphics... => 5
[5,1,1,1,1] generating graphics... => 5
[4,4,1] generating graphics... => 5
[4,3,2] generating graphics... => 4
[4,3,1,1] generating graphics... => 4
[4,2,2,1] generating graphics... => 4
[4,2,1,1,1] generating graphics... => 5
[4,1,1,1,1,1] generating graphics... => 6
[3,3,3] generating graphics... => 5
[3,3,2,1] generating graphics... => 4
[3,3,1,1,1] generating graphics... => 5
[3,2,2,2] generating graphics... => 5
[3,2,2,1,1] generating graphics... => 5
[3,2,1,1,1,1] generating graphics... => 6
[3,1,1,1,1,1,1] generating graphics... => 7
[2,2,2,2,1] generating graphics... => 5
[2,2,2,1,1,1] generating graphics... => 6
[2,2,1,1,1,1,1] generating graphics... => 7
[2,1,1,1,1,1,1,1] generating graphics... => 8
[1,1,1,1,1,1,1,1,1] generating graphics... => 9
[10] generating graphics... => 10
[9,1] generating graphics... => 9
[8,2] generating graphics... => 8
[8,1,1] generating graphics... => 8
[7,3] generating graphics... => 7
[7,2,1] generating graphics... => 7
[7,1,1,1] generating graphics... => 7
[6,4] generating graphics... => 6
[6,3,1] generating graphics... => 6
[6,2,2] generating graphics... => 6
[6,2,1,1] generating graphics... => 6
[6,1,1,1,1] generating graphics... => 6
[5,5] generating graphics... => 6
[5,4,1] generating graphics... => 5
[5,3,2] generating graphics... => 5
[5,3,1,1] generating graphics... => 5
[5,2,2,1] generating graphics... => 5
[5,2,1,1,1] generating graphics... => 5
[5,1,1,1,1,1] generating graphics... => 6
[4,4,2] generating graphics... => 5
[4,4,1,1] generating graphics... => 5
[4,3,3] generating graphics... => 5
[4,3,2,1] generating graphics... => 4
[4,3,1,1,1] generating graphics... => 5
[4,2,2,2] generating graphics... => 5
[4,2,2,1,1] generating graphics... => 5
[4,2,1,1,1,1] generating graphics... => 6
[4,1,1,1,1,1,1] generating graphics... => 7
[3,3,3,1] generating graphics... => 5
[3,3,2,2] generating graphics... => 5
[3,3,2,1,1] generating graphics... => 5
[3,3,1,1,1,1] generating graphics... => 6
[3,2,2,2,1] generating graphics... => 5
[3,2,2,1,1,1] generating graphics... => 6
[3,2,1,1,1,1,1] generating graphics... => 7
[3,1,1,1,1,1,1,1] generating graphics... => 8
[2,2,2,2,2] generating graphics... => 6
[2,2,2,2,1,1] generating graphics... => 6
[2,2,2,1,1,1,1] generating graphics... => 7
[2,2,1,1,1,1,1,1] generating graphics... => 8
[2,1,1,1,1,1,1,1,1] generating graphics... => 9
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 10
[11] generating graphics... => 11
[10,1] generating graphics... => 10
[9,2] generating graphics... => 9
[9,1,1] generating graphics... => 9
[8,3] generating graphics... => 8
[8,2,1] generating graphics... => 8
[8,1,1,1] generating graphics... => 8
[7,4] generating graphics... => 7
[7,3,1] generating graphics... => 7
[7,2,2] generating graphics... => 7
[7,2,1,1] generating graphics... => 7
[7,1,1,1,1] generating graphics... => 7
[6,5] generating graphics... => 6
[6,4,1] generating graphics... => 6
[6,3,2] generating graphics... => 6
[6,3,1,1] generating graphics... => 6
[6,2,2,1] generating graphics... => 6
[6,2,1,1,1] generating graphics... => 6
[6,1,1,1,1,1] generating graphics... => 6
[5,5,1] generating graphics... => 6
[5,4,2] generating graphics... => 5
[5,4,1,1] generating graphics... => 5
[5,3,3] generating graphics... => 5
[5,3,2,1] generating graphics... => 5
[5,3,1,1,1] generating graphics... => 5
[5,2,2,2] generating graphics... => 5
[5,2,2,1,1] generating graphics... => 5
[5,2,1,1,1,1] generating graphics... => 6
[5,1,1,1,1,1,1] generating graphics... => 7
[4,4,3] generating graphics... => 5
[4,4,2,1] generating graphics... => 5
[4,4,1,1,1] generating graphics... => 5
[4,3,3,1] generating graphics... => 5
[4,3,2,2] generating graphics... => 5
[4,3,2,1,1] generating graphics... => 5
[4,3,1,1,1,1] generating graphics... => 6
[4,2,2,2,1] generating graphics... => 5
[4,2,2,1,1,1] generating graphics... => 6
[4,2,1,1,1,1,1] generating graphics... => 7
[4,1,1,1,1,1,1,1] generating graphics... => 8
[3,3,3,2] generating graphics... => 5
[3,3,3,1,1] generating graphics... => 5
[3,3,2,2,1] generating graphics... => 5
[3,3,2,1,1,1] generating graphics... => 6
[3,3,1,1,1,1,1] generating graphics... => 7
[3,2,2,2,2] generating graphics... => 6
[3,2,2,2,1,1] generating graphics... => 6
[3,2,2,1,1,1,1] generating graphics... => 7
[3,2,1,1,1,1,1,1] generating graphics... => 8
[3,1,1,1,1,1,1,1,1] generating graphics... => 9
[2,2,2,2,2,1] generating graphics... => 6
[2,2,2,2,1,1,1] generating graphics... => 7
[2,2,2,1,1,1,1,1] generating graphics... => 8
[2,2,1,1,1,1,1,1,1] generating graphics... => 9
[2,1,1,1,1,1,1,1,1,1] generating graphics... => 10
[1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 11
[12] generating graphics... => 12
[11,1] generating graphics... => 11
[10,2] generating graphics... => 10
[10,1,1] generating graphics... => 10
[9,3] generating graphics... => 9
[9,2,1] generating graphics... => 9
[9,1,1,1] generating graphics... => 9
[8,4] generating graphics... => 8
[8,3,1] generating graphics... => 8
[8,2,2] generating graphics... => 8
[8,2,1,1] generating graphics... => 8
[8,1,1,1,1] generating graphics... => 8
[7,5] generating graphics... => 7
[7,4,1] generating graphics... => 7
[7,3,2] generating graphics... => 7
[7,3,1,1] generating graphics... => 7
[7,2,2,1] generating graphics... => 7
[7,2,1,1,1] generating graphics... => 7
[7,1,1,1,1,1] generating graphics... => 7
[6,6] generating graphics... => 7
[6,5,1] generating graphics... => 6
[6,4,2] generating graphics... => 6
[6,4,1,1] generating graphics... => 6
[6,3,3] generating graphics... => 6
[6,3,2,1] generating graphics... => 6
[6,3,1,1,1] generating graphics... => 6
[6,2,2,2] generating graphics... => 6
[6,2,2,1,1] generating graphics... => 6
[6,2,1,1,1,1] generating graphics... => 6
[6,1,1,1,1,1,1] generating graphics... => 7
[5,5,2] generating graphics... => 6
[5,5,1,1] generating graphics... => 6
[5,4,3] generating graphics... => 5
[5,4,2,1] generating graphics... => 5
[5,4,1,1,1] generating graphics... => 5
[5,3,3,1] generating graphics... => 5
[5,3,2,2] generating graphics... => 5
[5,3,2,1,1] generating graphics... => 5
[5,3,1,1,1,1] generating graphics... => 6
[5,2,2,2,1] generating graphics... => 5
[5,2,2,1,1,1] generating graphics... => 6
[5,2,1,1,1,1,1] generating graphics... => 7
[5,1,1,1,1,1,1,1] generating graphics... => 8
[4,4,4] generating graphics... => 6
[4,4,3,1] generating graphics... => 5
[4,4,2,2] generating graphics... => 5
[4,4,2,1,1] generating graphics... => 5
[4,4,1,1,1,1] generating graphics... => 6
[4,3,3,2] generating graphics... => 5
[4,3,3,1,1] generating graphics... => 5
[4,3,2,2,1] generating graphics... => 5
[4,3,2,1,1,1] generating graphics... => 6
[4,3,1,1,1,1,1] generating graphics... => 7
[4,2,2,2,2] generating graphics... => 6
[4,2,2,2,1,1] generating graphics... => 6
[4,2,2,1,1,1,1] generating graphics... => 7
[4,2,1,1,1,1,1,1] generating graphics... => 8
[4,1,1,1,1,1,1,1,1] generating graphics... => 9
[3,3,3,3] generating graphics... => 6
[3,3,3,2,1] generating graphics... => 5
[3,3,3,1,1,1] generating graphics... => 6
[3,3,2,2,2] generating graphics... => 6
[3,3,2,2,1,1] generating graphics... => 6
[3,3,2,1,1,1,1] generating graphics... => 7
[3,3,1,1,1,1,1,1] generating graphics... => 8
[3,2,2,2,2,1] generating graphics... => 6
[3,2,2,2,1,1,1] generating graphics... => 7
[3,2,2,1,1,1,1,1] generating graphics... => 8
[3,2,1,1,1,1,1,1,1] generating graphics... => 9
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 10
[2,2,2,2,2,2] generating graphics... => 7
[2,2,2,2,2,1,1] generating graphics... => 7
[2,2,2,2,1,1,1,1] generating graphics... => 8
[2,2,2,1,1,1,1,1,1] generating graphics... => 9
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 10
[2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 11
[1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 12
[5,4,3,1] generating graphics... => 5
[5,4,2,2] generating graphics... => 5
[5,4,2,1,1] generating graphics... => 5
[5,3,3,2] generating graphics... => 5
[5,3,3,1,1] generating graphics... => 5
[5,3,2,2,1] generating graphics... => 5
[4,4,3,2] generating graphics... => 5
[4,4,3,1,1] generating graphics... => 5
[4,4,2,2,1] generating graphics... => 5
[4,3,3,2,1] generating graphics... => 5
[5,4,3,2] generating graphics... => 5
[5,4,3,1,1] generating graphics... => 5
[5,4,2,2,1] generating graphics... => 5
[5,3,3,2,1] generating graphics... => 5
[4,4,3,2,1] generating graphics... => 5
[5,4,3,2,1] generating graphics... => 5
click to show generating function       
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 the perimeter of the largest rectangle that fits inside 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