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-----------------------------------------------------------------------------
Statistic identifier: St001214
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The aft of an integer partition.
The aft is the size of the partition minus the length of the first row or column, whichever is larger.
See also [[St000784]].
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(L):
if L:
return sum(L)-max(L[0],len(L))
else:
return 0
-----------------------------------------------------------------------------
Statistic values:
[] => 0
[1] => 0
[2] => 0
[1,1] => 0
[3] => 0
[2,1] => 1
[1,1,1] => 0
[4] => 0
[3,1] => 1
[2,2] => 2
[2,1,1] => 1
[1,1,1,1] => 0
[5] => 0
[4,1] => 1
[3,2] => 2
[3,1,1] => 2
[2,2,1] => 2
[2,1,1,1] => 1
[1,1,1,1,1] => 0
[6] => 0
[5,1] => 1
[4,2] => 2
[4,1,1] => 2
[3,3] => 3
[3,2,1] => 3
[3,1,1,1] => 2
[2,2,2] => 3
[2,2,1,1] => 2
[2,1,1,1,1] => 1
[1,1,1,1,1,1] => 0
[7] => 0
[6,1] => 1
[5,2] => 2
[5,1,1] => 2
[4,3] => 3
[4,2,1] => 3
[4,1,1,1] => 3
[3,3,1] => 4
[3,2,2] => 4
[3,2,1,1] => 3
[3,1,1,1,1] => 2
[2,2,2,1] => 3
[2,2,1,1,1] => 2
[2,1,1,1,1,1] => 1
[1,1,1,1,1,1,1] => 0
[8] => 0
[7,1] => 1
[6,2] => 2
[6,1,1] => 2
[5,3] => 3
[5,2,1] => 3
[5,1,1,1] => 3
[4,4] => 4
[4,3,1] => 4
[4,2,2] => 4
[4,2,1,1] => 4
[4,1,1,1,1] => 3
[3,3,2] => 5
[3,3,1,1] => 4
[3,2,2,1] => 4
[3,2,1,1,1] => 3
[3,1,1,1,1,1] => 2
[2,2,2,2] => 4
[2,2,2,1,1] => 3
[2,2,1,1,1,1] => 2
[2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1] => 0
[9] => 0
[8,1] => 1
[7,2] => 2
[7,1,1] => 2
[6,3] => 3
[6,2,1] => 3
[6,1,1,1] => 3
[5,4] => 4
[5,3,1] => 4
[5,2,2] => 4
[5,2,1,1] => 4
[5,1,1,1,1] => 4
[4,4,1] => 5
[4,3,2] => 5
[4,3,1,1] => 5
[4,2,2,1] => 5
[4,2,1,1,1] => 4
[4,1,1,1,1,1] => 3
[3,3,3] => 6
[3,3,2,1] => 5
[3,3,1,1,1] => 4
[3,2,2,2] => 5
[3,2,2,1,1] => 4
[3,2,1,1,1,1] => 3
[3,1,1,1,1,1,1] => 2
[2,2,2,2,1] => 4
[2,2,2,1,1,1] => 3
[2,2,1,1,1,1,1] => 2
[2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1] => 0
[10] => 0
[9,1] => 1
[8,2] => 2
[8,1,1] => 2
[7,3] => 3
[7,2,1] => 3
[7,1,1,1] => 3
[6,4] => 4
[6,3,1] => 4
[6,2,2] => 4
[6,2,1,1] => 4
[6,1,1,1,1] => 4
[5,5] => 5
[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] => 4
[4,4,2] => 6
[4,4,1,1] => 6
[4,3,3] => 6
[4,3,2,1] => 6
[4,3,1,1,1] => 5
[4,2,2,2] => 6
[4,2,2,1,1] => 5
[4,2,1,1,1,1] => 4
[4,1,1,1,1,1,1] => 3
[3,3,3,1] => 6
[3,3,2,2] => 6
[3,3,2,1,1] => 5
[3,3,1,1,1,1] => 4
[3,2,2,2,1] => 5
[3,2,2,1,1,1] => 4
[3,2,1,1,1,1,1] => 3
[3,1,1,1,1,1,1,1] => 2
[2,2,2,2,2] => 5
[2,2,2,2,1,1] => 4
[2,2,2,1,1,1,1] => 3
[2,2,1,1,1,1,1,1] => 2
[2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1] => 0
[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
[4,4,3] => 7
[4,4,2,1] => 7
[4,4,1,1,1] => 6
[4,3,3,1] => 7
[4,3,2,2] => 7
[4,3,2,1,1] => 6
[4,2,2,2,1] => 6
[3,3,3,2] => 7
[3,3,3,1,1] => 6
[3,3,2,2,1] => 6
[6,4,2] => 6
[5,4,3] => 7
[5,4,2,1] => 7
[5,4,1,1,1] => 7
[5,3,3,1] => 7
[5,3,2,2] => 7
[5,3,2,1,1] => 7
[5,2,2,2,1] => 7
[4,4,3,1] => 8
[4,4,2,2] => 8
[4,4,2,1,1] => 7
[4,3,3,2] => 8
[4,3,3,1,1] => 7
[4,3,2,2,1] => 7
[3,3,3,2,1] => 7
[3,3,2,2,1,1] => 6
[5,4,3,1] => 8
[5,4,2,2] => 8
[5,4,2,1,1] => 8
[5,3,3,2] => 8
[5,3,3,1,1] => 8
[5,3,2,2,1] => 8
[4,4,3,2] => 9
[4,4,3,1,1] => 8
[4,4,2,2,1] => 8
[4,3,3,2,1] => 8
[5,4,3,2] => 9
[5,4,3,1,1] => 9
[5,4,2,2,1] => 9
[5,3,3,2,1] => 9
[4,4,3,2,1] => 9
[5,4,3,2,1] => 10
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Created: Jun 21, 2018 at 00:45 by Sara Billey
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Last Updated: Jan 22, 2023 at 11:54 by Martin Rubey