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Identifier
Values
=>
Cc0002;cc-rep
[]=>0 [1]=>0 [2]=>0 [1,1]=>0 [3]=>1 [2,1]=>1 [1,1,1]=>1 [4]=>1 [3,1]=>0 [2,2]=>1 [2,1,1]=>0 [1,1,1,1]=>1 [5]=>1 [4,1]=>1 [3,2]=>1 [3,1,1]=>0 [2,2,1]=>1 [2,1,1,1]=>1 [1,1,1,1,1]=>1 [6]=>2 [5,1]=>2 [4,2]=>0 [4,1,1]=>2 [3,3]=>2 [3,2,1]=>2 [3,1,1,1]=>2 [2,2,2]=>2 [2,2,1,1]=>0 [2,1,1,1,1]=>2 [1,1,1,1,1,1]=>2 [7]=>2 [6,1]=>1 [5,2]=>2 [5,1,1]=>1 [4,3]=>2 [4,2,1]=>2 [4,1,1,1]=>2 [3,3,1]=>1 [3,2,2]=>1 [3,2,1,1]=>2 [3,1,1,1,1]=>1 [2,2,2,1]=>2 [2,2,1,1,1]=>2 [2,1,1,1,1,1]=>1 [1,1,1,1,1,1,1]=>2 [8]=>2 [7,1]=>2 [6,2]=>2 [6,1,1]=>1 [5,3]=>2 [5,2,1]=>2 [5,1,1,1]=>2 [4,4]=>2 [4,3,1]=>2 [4,2,2]=>2 [4,2,1,1]=>0 [4,1,1,1,1]=>2 [3,3,2]=>1 [3,3,1,1]=>2 [3,2,2,1]=>2 [3,2,1,1,1]=>2 [3,1,1,1,1,1]=>1 [2,2,2,2]=>2 [2,2,2,1,1]=>2 [2,2,1,1,1,1]=>2 [2,1,1,1,1,1,1]=>2 [1,1,1,1,1,1,1,1]=>2 [9]=>3 [8,1]=>3 [7,2]=>1 [7,1,1]=>3 [6,3]=>3 [6,2,1]=>3 [6,1,1,1]=>3 [5,4]=>3 [5,3,1]=>0 [5,2,2]=>3 [5,2,1,1]=>1 [5,1,1,1,1]=>3 [4,4,1]=>3 [4,3,2]=>3 [4,3,1,1]=>1 [4,2,2,1]=>1 [4,2,1,1,1]=>1 [4,1,1,1,1,1]=>3 [3,3,3]=>3 [3,3,2,1]=>3 [3,3,1,1,1]=>3 [3,2,2,2]=>3 [3,2,2,1,1]=>0 [3,2,1,1,1,1]=>3 [3,1,1,1,1,1,1]=>3 [2,2,2,2,1]=>3 [2,2,2,1,1,1]=>3 [2,2,1,1,1,1,1]=>1 [2,1,1,1,1,1,1,1]=>3 [1,1,1,1,1,1,1,1,1]=>3 [10]=>3 [9,1]=>2 [8,2]=>3 [8,1,1]=>2 [7,3]=>3 [7,2,1]=>3 [7,1,1,1]=>3 [6,4]=>2 [6,3,1]=>2 [6,2,2]=>2 [6,2,1,1]=>3 [6,1,1,1,1]=>2 [5,5]=>3 [5,4,1]=>2 [5,3,2]=>2 [5,3,1,1]=>0 [5,2,2,1]=>3 [5,2,1,1,1]=>3 [5,1,1,1,1,1]=>2 [4,4,2]=>2 [4,4,1,1]=>3 [4,3,3]=>3 [4,3,2,1]=>3 [4,3,1,1,1]=>3 [4,2,2,2]=>3 [4,2,2,1,1]=>0 [4,2,1,1,1,1]=>3 [4,1,1,1,1,1,1]=>3 [3,3,3,1]=>3 [3,3,2,2]=>2 [3,3,2,1,1]=>2 [3,3,1,1,1,1]=>2 [3,2,2,2,1]=>2 [3,2,2,1,1,1]=>2 [3,2,1,1,1,1,1]=>3 [3,1,1,1,1,1,1,1]=>2 [2,2,2,2,2]=>3 [2,2,2,2,1,1]=>2 [2,2,2,1,1,1,1]=>3 [2,2,1,1,1,1,1,1]=>3 [2,1,1,1,1,1,1,1,1]=>2 [1,1,1,1,1,1,1,1,1,1]=>3 [11]=>3 [10,1]=>3 [9,2]=>3 [9,1,1]=>2 [8,3]=>3 [8,2,1]=>3 [8,1,1,1]=>3 [7,4]=>3 [7,3,1]=>3 [7,2,2]=>3 [7,2,1,1]=>1 [7,1,1,1,1]=>3 [6,5]=>3 [6,4,1]=>2 [6,3,2]=>2 [6,3,1,1]=>3 [6,2,2,1]=>3 [6,2,1,1,1]=>3 [6,1,1,1,1,1]=>2 [5,5,1]=>3 [5,4,2]=>2 [5,4,1,1]=>3 [5,3,3]=>3 [5,3,2,1]=>3 [5,3,1,1,1]=>3 [5,2,2,2]=>3 [5,2,2,1,1]=>3 [5,2,1,1,1,1]=>3 [5,1,1,1,1,1,1]=>3 [4,4,3]=>3 [4,4,2,1]=>3 [4,4,1,1,1]=>3 [4,3,3,1]=>1 [4,3,2,2]=>3 [4,3,2,1,1]=>3 [4,3,1,1,1,1]=>3 [4,2,2,2,1]=>3 [4,2,2,1,1,1]=>3 [4,2,1,1,1,1,1]=>1 [4,1,1,1,1,1,1,1]=>3 [3,3,3,2]=>3 [3,3,3,1,1]=>3 [3,3,2,2,1]=>2 [3,3,2,1,1,1]=>2 [3,3,1,1,1,1,1]=>3 [3,2,2,2,2]=>3 [3,2,2,2,1,1]=>2 [3,2,2,1,1,1,1]=>3 [3,2,1,1,1,1,1,1]=>3 [3,1,1,1,1,1,1,1,1]=>2 [2,2,2,2,2,1]=>3 [2,2,2,2,1,1,1]=>3 [2,2,2,1,1,1,1,1]=>3 [2,2,1,1,1,1,1,1,1]=>3 [2,1,1,1,1,1,1,1,1,1]=>3 [1,1,1,1,1,1,1,1,1,1,1]=>3 [12]=>4 [11,1]=>4 [10,2]=>2 [10,1,1]=>4 [9,3]=>4 [9,2,1]=>4 [9,1,1,1]=>4 [8,4]=>4 [8,3,1]=>1 [8,2,2]=>4 [8,2,1,1]=>2 [8,1,1,1,1]=>4 [7,5]=>2 [7,4,1]=>4 [7,3,2]=>4 [7,3,1,1]=>2 [7,2,2,1]=>2 [7,2,1,1,1]=>2 [7,1,1,1,1,1]=>4 [6,6]=>4 [6,5,1]=>4 [6,4,2]=>0 [6,4,1,1]=>4 [6,3,3]=>4 [6,3,2,1]=>4 [6,3,1,1,1]=>4 [6,2,2,2]=>4 [6,2,2,1,1]=>1 [6,2,1,1,1,1]=>4 [6,1,1,1,1,1,1]=>4 [5,5,2]=>4 [5,5,1,1]=>2 [5,4,3]=>4 [5,4,2,1]=>4 [5,4,1,1,1]=>4 [5,3,3,1]=>2 [5,3,2,2]=>1 [5,3,2,1,1]=>4 [5,3,1,1,1,1]=>1 [5,2,2,2,1]=>4 [5,2,2,1,1,1]=>4 [5,2,1,1,1,1,1]=>2 [5,1,1,1,1,1,1,1]=>4 [4,4,4]=>4 [4,4,3,1]=>2 [4,4,2,2]=>4 [4,4,2,1,1]=>1 [4,4,1,1,1,1]=>4 [4,3,3,2]=>2 [4,3,3,1,1]=>2 [4,3,2,2,1]=>4 [4,3,2,1,1,1]=>4 [4,3,1,1,1,1,1]=>2 [4,2,2,2,2]=>2 [4,2,2,2,1,1]=>4 [4,2,2,1,1,1,1]=>2 [4,2,1,1,1,1,1,1]=>2 [4,1,1,1,1,1,1,1,1]=>4 [3,3,3,3]=>4 [3,3,3,2,1]=>4 [3,3,3,1,1,1]=>4 [3,3,2,2,2]=>4 [3,3,2,2,1,1]=>0 [3,3,2,1,1,1,1]=>4 [3,3,1,1,1,1,1,1]=>4 [3,2,2,2,2,1]=>4 [3,2,2,2,1,1,1]=>4 [3,2,2,1,1,1,1,1]=>1 [3,2,1,1,1,1,1,1,1]=>4 [3,1,1,1,1,1,1,1,1,1]=>4 [2,2,2,2,2,2]=>4 [2,2,2,2,2,1,1]=>2 [2,2,2,2,1,1,1,1]=>4 [2,2,2,1,1,1,1,1,1]=>4 [2,2,1,1,1,1,1,1,1,1]=>2 [2,1,1,1,1,1,1,1,1,1,1]=>4 [1,1,1,1,1,1,1,1,1,1,1,1]=>4 [5,4,3,1]=>4 [5,4,2,2]=>3 [5,4,2,1,1]=>3 [5,3,3,2]=>1 [5,3,3,1,1]=>4 [5,3,2,2,1]=>3 [4,4,3,2]=>4 [4,4,3,1,1]=>1 [4,4,2,2,1]=>3 [4,3,3,2,1]=>4 [5,4,3,2]=>4 [5,4,3,1,1]=>4 [5,4,2,2,1]=>3 [5,3,3,2,1]=>4 [4,4,3,2,1]=>4 [5,4,3,2,1]=>5
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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