Identifier
Identifier
Values
[] generating graphics... => 0
[1] generating graphics... => 0
[2] generating graphics... => 0
[1,1] generating graphics... => 0
[3] generating graphics... => 1
[2,1] generating graphics... => 1
[1,1,1] generating graphics... => 1
[4] generating graphics... => 1
[3,1] generating graphics... => 0
[2,2] generating graphics... => 1
[2,1,1] generating graphics... => 0
[1,1,1,1] generating graphics... => 1
[5] generating graphics... => 1
[4,1] generating graphics... => 1
[3,2] generating graphics... => 1
[3,1,1] generating graphics... => 0
[2,2,1] generating graphics... => 1
[2,1,1,1] generating graphics... => 1
[1,1,1,1,1] generating graphics... => 1
[6] generating graphics... => 2
[5,1] generating graphics... => 2
[4,2] generating graphics... => 0
[4,1,1] generating graphics... => 2
[3,3] generating graphics... => 2
[3,2,1] generating graphics... => 2
[3,1,1,1] generating graphics... => 2
[2,2,2] generating graphics... => 2
[2,2,1,1] generating graphics... => 0
[2,1,1,1,1] generating graphics... => 2
[1,1,1,1,1,1] generating graphics... => 2
[7] generating graphics... => 2
[6,1] generating graphics... => 1
[5,2] generating graphics... => 2
[5,1,1] generating graphics... => 1
[4,3] generating graphics... => 2
[4,2,1] generating graphics... => 2
[4,1,1,1] generating graphics... => 2
[3,3,1] generating graphics... => 1
[3,2,2] generating graphics... => 1
[3,2,1,1] generating graphics... => 2
[3,1,1,1,1] generating graphics... => 1
[2,2,2,1] generating graphics... => 2
[2,2,1,1,1] generating graphics... => 2
[2,1,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1,1] generating graphics... => 2
[8] generating graphics... => 2
[7,1] generating graphics... => 2
[6,2] generating graphics... => 2
[6,1,1] generating graphics... => 1
[5,3] generating graphics... => 2
[5,2,1] generating graphics... => 2
[5,1,1,1] generating graphics... => 2
[4,4] generating graphics... => 2
[4,3,1] generating graphics... => 2
[4,2,2] generating graphics... => 2
[4,2,1,1] generating graphics... => 0
[4,1,1,1,1] generating graphics... => 2
[3,3,2] generating graphics... => 1
[3,3,1,1] generating graphics... => 2
[3,2,2,1] generating graphics... => 2
[3,2,1,1,1] generating graphics... => 2
[3,1,1,1,1,1] generating graphics... => 1
[2,2,2,2] generating graphics... => 2
[2,2,2,1,1] generating graphics... => 2
[2,2,1,1,1,1] generating graphics... => 2
[2,1,1,1,1,1,1] generating graphics... => 2
[1,1,1,1,1,1,1,1] generating graphics... => 2
[9] generating graphics... => 3
[8,1] generating graphics... => 3
[7,2] generating graphics... => 1
[7,1,1] generating graphics... => 3
[6,3] generating graphics... => 3
[6,2,1] generating graphics... => 3
[6,1,1,1] generating graphics... => 3
[5,4] generating graphics... => 3
[5,3,1] generating graphics... => 0
[5,2,2] generating graphics... => 3
[5,2,1,1] generating graphics... => 1
[5,1,1,1,1] generating graphics... => 3
[4,4,1] generating graphics... => 3
[4,3,2] generating graphics... => 3
[4,3,1,1] generating graphics... => 1
[4,2,2,1] generating graphics... => 1
[4,2,1,1,1] generating graphics... => 1
[4,1,1,1,1,1] generating graphics... => 3
[3,3,3] generating graphics... => 3
[3,3,2,1] generating graphics... => 3
[3,3,1,1,1] generating graphics... => 3
[3,2,2,2] generating graphics... => 3
[3,2,2,1,1] generating graphics... => 0
[3,2,1,1,1,1] generating graphics... => 3
[3,1,1,1,1,1,1] generating graphics... => 3
[2,2,2,2,1] generating graphics... => 3
[2,2,2,1,1,1] generating graphics... => 3
[2,2,1,1,1,1,1] generating graphics... => 1
[2,1,1,1,1,1,1,1] generating graphics... => 3
[1,1,1,1,1,1,1,1,1] generating graphics... => 3
[10] generating graphics... => 3
[9,1] generating graphics... => 2
[8,2] generating graphics... => 3
[8,1,1] generating graphics... => 2
[7,3] generating graphics... => 3
[7,2,1] generating graphics... => 3
[7,1,1,1] generating graphics... => 3
[6,4] generating graphics... => 2
[6,3,1] generating graphics... => 2
[6,2,2] generating graphics... => 2
[6,2,1,1] generating graphics... => 3
[6,1,1,1,1] generating graphics... => 2
[5,5] generating graphics... => 3
[5,4,1] generating graphics... => 2
[5,3,2] generating graphics... => 2
[5,3,1,1] generating graphics... => 0
[5,2,2,1] generating graphics... => 3
[5,2,1,1,1] generating graphics... => 3
[5,1,1,1,1,1] generating graphics... => 2
[4,4,2] generating graphics... => 2
[4,4,1,1] generating graphics... => 3
[4,3,3] generating graphics... => 3
[4,3,2,1] generating graphics... => 3
[4,3,1,1,1] generating graphics... => 3
[4,2,2,2] generating graphics... => 3
[4,2,2,1,1] generating graphics... => 0
[4,2,1,1,1,1] generating graphics... => 3
[4,1,1,1,1,1,1] generating graphics... => 3
[3,3,3,1] generating graphics... => 3
[3,3,2,2] generating graphics... => 2
[3,3,2,1,1] generating graphics... => 2
[3,3,1,1,1,1] generating graphics... => 2
[3,2,2,2,1] generating graphics... => 2
[3,2,2,1,1,1] generating graphics... => 2
[3,2,1,1,1,1,1] generating graphics... => 3
[3,1,1,1,1,1,1,1] generating graphics... => 2
[2,2,2,2,2] generating graphics... => 3
[2,2,2,2,1,1] generating graphics... => 2
[2,2,2,1,1,1,1] generating graphics... => 3
[2,2,1,1,1,1,1,1] generating graphics... => 3
[2,1,1,1,1,1,1,1,1] generating graphics... => 2
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 3
[11] generating graphics... => 3
[10,1] generating graphics... => 3
[9,2] generating graphics... => 3
[9,1,1] generating graphics... => 2
[8,3] generating graphics... => 3
[8,2,1] generating graphics... => 3
[8,1,1,1] generating graphics... => 3
[7,4] generating graphics... => 3
[7,3,1] generating graphics... => 3
[7,2,2] generating graphics... => 3
[7,2,1,1] generating graphics... => 1
[7,1,1,1,1] generating graphics... => 3
[6,5] generating graphics... => 3
[6,4,1] generating graphics... => 2
[6,3,2] generating graphics... => 2
[6,3,1,1] generating graphics... => 3
[6,2,2,1] generating graphics... => 3
[6,2,1,1,1] generating graphics... => 3
[6,1,1,1,1,1] generating graphics... => 2
[5,5,1] generating graphics... => 3
[5,4,2] generating graphics... => 2
[5,4,1,1] generating graphics... => 3
[5,3,3] generating graphics... => 3
[5,3,2,1] generating graphics... => 3
[5,3,1,1,1] generating graphics... => 3
[5,2,2,2] generating graphics... => 3
[5,2,2,1,1] generating graphics... => 3
[5,2,1,1,1,1] generating graphics... => 3
[5,1,1,1,1,1,1] generating graphics... => 3
[4,4,3] generating graphics... => 3
[4,4,2,1] generating graphics... => 3
[4,4,1,1,1] generating graphics... => 3
[4,3,3,1] generating graphics... => 1
[4,3,2,2] generating graphics... => 3
[4,3,2,1,1] generating graphics... => 3
[4,3,1,1,1,1] generating graphics... => 3
[4,2,2,2,1] generating graphics... => 3
[4,2,2,1,1,1] generating graphics... => 3
[4,2,1,1,1,1,1] generating graphics... => 1
[4,1,1,1,1,1,1,1] generating graphics... => 3
[3,3,3,2] generating graphics... => 3
[3,3,3,1,1] generating graphics... => 3
[3,3,2,2,1] generating graphics... => 2
[3,3,2,1,1,1] generating graphics... => 2
[3,3,1,1,1,1,1] generating graphics... => 3
[3,2,2,2,2] generating graphics... => 3
[3,2,2,2,1,1] generating graphics... => 2
[3,2,2,1,1,1,1] generating graphics... => 3
[3,2,1,1,1,1,1,1] generating graphics... => 3
[3,1,1,1,1,1,1,1,1] generating graphics... => 2
[2,2,2,2,2,1] generating graphics... => 3
[2,2,2,2,1,1,1] generating graphics... => 3
[2,2,2,1,1,1,1,1] generating graphics... => 3
[2,2,1,1,1,1,1,1,1] generating graphics... => 3
[2,1,1,1,1,1,1,1,1,1] generating graphics... => 3
[1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 3
[12] generating graphics... => 4
[11,1] generating graphics... => 4
[10,2] generating graphics... => 2
[10,1,1] generating graphics... => 4
[9,3] generating graphics... => 4
[9,2,1] generating graphics... => 4
[9,1,1,1] generating graphics... => 4
[8,4] generating graphics... => 4
[8,3,1] generating graphics... => 1
[8,2,2] generating graphics... => 4
[8,2,1,1] generating graphics... => 2
[8,1,1,1,1] generating graphics... => 4
[7,5] generating graphics... => 2
[7,4,1] generating graphics... => 4
[7,3,2] generating graphics... => 4
[7,3,1,1] generating graphics... => 2
[7,2,2,1] generating graphics... => 2
[7,2,1,1,1] generating graphics... => 2
[7,1,1,1,1,1] generating graphics... => 4
[6,6] generating graphics... => 4
[6,5,1] generating graphics... => 4
[6,4,2] generating graphics... => 0
[6,4,1,1] generating graphics... => 4
[6,3,3] generating graphics... => 4
[6,3,2,1] generating graphics... => 4
[6,3,1,1,1] generating graphics... => 4
[6,2,2,2] generating graphics... => 4
[6,2,2,1,1] generating graphics... => 1
[6,2,1,1,1,1] generating graphics... => 4
[6,1,1,1,1,1,1] generating graphics... => 4
[5,5,2] generating graphics... => 4
[5,5,1,1] generating graphics... => 2
[5,4,3] generating graphics... => 4
[5,4,2,1] generating graphics... => 4
[5,4,1,1,1] generating graphics... => 4
[5,3,3,1] generating graphics... => 2
[5,3,2,2] generating graphics... => 1
[5,3,2,1,1] generating graphics... => 4
[5,3,1,1,1,1] generating graphics... => 1
[5,2,2,2,1] generating graphics... => 4
[5,2,2,1,1,1] generating graphics... => 4
[5,2,1,1,1,1,1] generating graphics... => 2
[5,1,1,1,1,1,1,1] generating graphics... => 4
[4,4,4] generating graphics... => 4
[4,4,3,1] generating graphics... => 2
[4,4,2,2] generating graphics... => 4
[4,4,2,1,1] generating graphics... => 1
[4,4,1,1,1,1] generating graphics... => 4
[4,3,3,2] generating graphics... => 2
[4,3,3,1,1] generating graphics... => 2
[4,3,2,2,1] generating graphics... => 4
[4,3,2,1,1,1] generating graphics... => 4
[4,3,1,1,1,1,1] generating graphics... => 2
[4,2,2,2,2] generating graphics... => 2
[4,2,2,2,1,1] generating graphics... => 4
[4,2,2,1,1,1,1] generating graphics... => 2
[4,2,1,1,1,1,1,1] generating graphics... => 2
[4,1,1,1,1,1,1,1,1] generating graphics... => 4
[3,3,3,3] generating graphics... => 4
[3,3,3,2,1] generating graphics... => 4
[3,3,3,1,1,1] generating graphics... => 4
[3,3,2,2,2] generating graphics... => 4
[3,3,2,2,1,1] generating graphics... => 0
[3,3,2,1,1,1,1] generating graphics... => 4
[3,3,1,1,1,1,1,1] generating graphics... => 4
[3,2,2,2,2,1] generating graphics... => 4
[3,2,2,2,1,1,1] generating graphics... => 4
[3,2,2,1,1,1,1,1] generating graphics... => 1
[3,2,1,1,1,1,1,1,1] generating graphics... => 4
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 4
[2,2,2,2,2,2] generating graphics... => 4
[2,2,2,2,2,1,1] generating graphics... => 2
[2,2,2,2,1,1,1,1] generating graphics... => 4
[2,2,2,1,1,1,1,1,1] generating graphics... => 4
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 2
[2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 4
[1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 4
[5,4,3,1] generating graphics... => 4
[5,4,2,2] generating graphics... => 3
[5,4,2,1,1] generating graphics... => 3
[5,3,3,2] generating graphics... => 1
[5,3,3,1,1] generating graphics... => 4
[5,3,2,2,1] generating graphics... => 3
[4,4,3,2] generating graphics... => 4
[4,4,3,1,1] generating graphics... => 1
[4,4,2,2,1] generating graphics... => 3
[4,3,3,2,1] generating graphics... => 4
[5,4,3,2] generating graphics... => 4
[5,4,3,1,1] generating graphics... => 4
[5,4,2,2,1] generating graphics... => 3
[5,3,3,2,1] generating graphics... => 4
[4,4,3,2,1] generating graphics... => 4
[5,4,3,2,1] generating graphics... => 5
click to show generating function       
Description
The number of 3-rim hooks removed from an integer partition to obtain its associated 3-core.
For any positive integer $k$, one associates a $k$-core to a partition by repeatedly removing all rim hooks of size $k$.
This statistic counts the $3$-rim hooks that are removed in this process to obtain a $3$-core.
Code
def statistic(L):
    k = 3
    return (sum(L)-sum(L.core(k)))/k
Created
Feb 20, 2017 at 10:33 by Christian Stump
Updated
Jan 11, 2018 at 13:06 by Martin Rubey