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-----------------------------------------------------------------------------
Statistic identifier: St001091
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The number of parts in an integer partition whose next smaller part has the same size.
In other words, this is the number of distinct parts subtracted from the number of all parts.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(L):
return len(L) - len(set(L))
-----------------------------------------------------------------------------
Statistic values:
[] => 0
[1] => 0
[2] => 0
[1,1] => 1
[3] => 0
[2,1] => 0
[1,1,1] => 2
[4] => 0
[3,1] => 0
[2,2] => 1
[2,1,1] => 1
[1,1,1,1] => 3
[5] => 0
[4,1] => 0
[3,2] => 0
[3,1,1] => 1
[2,2,1] => 1
[2,1,1,1] => 2
[1,1,1,1,1] => 4
[6] => 0
[5,1] => 0
[4,2] => 0
[4,1,1] => 1
[3,3] => 1
[3,2,1] => 0
[3,1,1,1] => 2
[2,2,2] => 2
[2,2,1,1] => 2
[2,1,1,1,1] => 3
[1,1,1,1,1,1] => 5
[7] => 0
[6,1] => 0
[5,2] => 0
[5,1,1] => 1
[4,3] => 0
[4,2,1] => 0
[4,1,1,1] => 2
[3,3,1] => 1
[3,2,2] => 1
[3,2,1,1] => 1
[3,1,1,1,1] => 3
[2,2,2,1] => 2
[2,2,1,1,1] => 3
[2,1,1,1,1,1] => 4
[1,1,1,1,1,1,1] => 6
[8] => 0
[7,1] => 0
[6,2] => 0
[6,1,1] => 1
[5,3] => 0
[5,2,1] => 0
[5,1,1,1] => 2
[4,4] => 1
[4,3,1] => 0
[4,2,2] => 1
[4,2,1,1] => 1
[4,1,1,1,1] => 3
[3,3,2] => 1
[3,3,1,1] => 2
[3,2,2,1] => 1
[3,2,1,1,1] => 2
[3,1,1,1,1,1] => 4
[2,2,2,2] => 3
[2,2,2,1,1] => 3
[2,2,1,1,1,1] => 4
[2,1,1,1,1,1,1] => 5
[1,1,1,1,1,1,1,1] => 7
[9] => 0
[8,1] => 0
[7,2] => 0
[7,1,1] => 1
[6,3] => 0
[6,2,1] => 0
[6,1,1,1] => 2
[5,4] => 0
[5,3,1] => 0
[5,2,2] => 1
[5,2,1,1] => 1
[5,1,1,1,1] => 3
[4,4,1] => 1
[4,3,2] => 0
[4,3,1,1] => 1
[4,2,2,1] => 1
[4,2,1,1,1] => 2
[4,1,1,1,1,1] => 4
[3,3,3] => 2
[3,3,2,1] => 1
[3,3,1,1,1] => 3
[3,2,2,2] => 2
[3,2,2,1,1] => 2
[3,2,1,1,1,1] => 3
[3,1,1,1,1,1,1] => 5
[2,2,2,2,1] => 3
[2,2,2,1,1,1] => 4
[2,2,1,1,1,1,1] => 5
[2,1,1,1,1,1,1,1] => 6
[1,1,1,1,1,1,1,1,1] => 8
[10] => 0
[9,1] => 0
[8,2] => 0
[8,1,1] => 1
[7,3] => 0
[7,2,1] => 0
[7,1,1,1] => 2
[6,4] => 0
[6,3,1] => 0
[6,2,2] => 1
[6,2,1,1] => 1
[6,1,1,1,1] => 3
[5,5] => 1
[5,4,1] => 0
[5,3,2] => 0
[5,3,1,1] => 1
[5,2,2,1] => 1
[5,2,1,1,1] => 2
[5,1,1,1,1,1] => 4
[4,4,2] => 1
[4,4,1,1] => 2
[4,3,3] => 1
[4,3,2,1] => 0
[4,3,1,1,1] => 2
[4,2,2,2] => 2
[4,2,2,1,1] => 2
[4,2,1,1,1,1] => 3
[4,1,1,1,1,1,1] => 5
[3,3,3,1] => 2
[3,3,2,2] => 2
[3,3,2,1,1] => 2
[3,3,1,1,1,1] => 4
[3,2,2,2,1] => 2
[3,2,2,1,1,1] => 3
[3,2,1,1,1,1,1] => 4
[3,1,1,1,1,1,1,1] => 6
[2,2,2,2,2] => 4
[2,2,2,2,1,1] => 4
[2,2,2,1,1,1,1] => 5
[2,2,1,1,1,1,1,1] => 6
[2,1,1,1,1,1,1,1,1] => 7
[1,1,1,1,1,1,1,1,1,1] => 9
[11] => 0
[10,1] => 0
[9,2] => 0
[9,1,1] => 1
[8,3] => 0
[8,2,1] => 0
[8,1,1,1] => 2
[7,4] => 0
[7,3,1] => 0
[7,2,2] => 1
[7,2,1,1] => 1
[7,1,1,1,1] => 3
[6,5] => 0
[6,4,1] => 0
[6,3,2] => 0
[6,3,1,1] => 1
[6,2,2,1] => 1
[6,2,1,1,1] => 2
[6,1,1,1,1,1] => 4
[5,5,1] => 1
[5,4,2] => 0
[5,4,1,1] => 1
[5,3,3] => 1
[5,3,2,1] => 0
[5,3,1,1,1] => 2
[5,2,2,2] => 2
[5,2,2,1,1] => 2
[5,2,1,1,1,1] => 3
[5,1,1,1,1,1,1] => 5
[4,4,3] => 1
[4,4,2,1] => 1
[4,4,1,1,1] => 3
[4,3,3,1] => 1
[4,3,2,2] => 1
[4,3,2,1,1] => 1
[4,3,1,1,1,1] => 3
[4,2,2,2,1] => 2
[4,2,2,1,1,1] => 3
[4,2,1,1,1,1,1] => 4
[4,1,1,1,1,1,1,1] => 6
[3,3,3,2] => 2
[3,3,3,1,1] => 3
[3,3,2,2,1] => 2
[3,3,2,1,1,1] => 3
[3,3,1,1,1,1,1] => 5
[3,2,2,2,2] => 3
[3,2,2,2,1,1] => 3
[3,2,2,1,1,1,1] => 4
[3,2,1,1,1,1,1,1] => 5
[3,1,1,1,1,1,1,1,1] => 7
[2,2,2,2,2,1] => 4
[2,2,2,2,1,1,1] => 5
[2,2,2,1,1,1,1,1] => 6
[2,2,1,1,1,1,1,1,1] => 7
[2,1,1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,1,1,1,1,1] => 10
[12] => 0
[11,1] => 0
[10,2] => 0
[10,1,1] => 1
[9,3] => 0
[9,2,1] => 0
[9,1,1,1] => 2
[8,4] => 0
[8,3,1] => 0
[8,2,2] => 1
[8,2,1,1] => 1
[8,1,1,1,1] => 3
[7,5] => 0
[7,4,1] => 0
[7,3,2] => 0
[7,3,1,1] => 1
[7,2,2,1] => 1
[7,2,1,1,1] => 2
[7,1,1,1,1,1] => 4
[6,6] => 1
[6,5,1] => 0
[6,4,2] => 0
[6,4,1,1] => 1
[6,3,3] => 1
[6,3,2,1] => 0
[6,3,1,1,1] => 2
[6,2,2,2] => 2
[6,2,2,1,1] => 2
[6,2,1,1,1,1] => 3
[6,1,1,1,1,1,1] => 5
[5,5,2] => 1
[5,5,1,1] => 2
[5,4,3] => 0
[5,4,2,1] => 0
[5,4,1,1,1] => 2
[5,3,3,1] => 1
[5,3,2,2] => 1
[5,3,2,1,1] => 1
[5,3,1,1,1,1] => 3
[5,2,2,2,1] => 2
[5,2,2,1,1,1] => 3
[5,2,1,1,1,1,1] => 4
[5,1,1,1,1,1,1,1] => 6
[4,4,4] => 2
[4,4,3,1] => 1
[4,4,2,2] => 2
[4,4,2,1,1] => 2
[4,4,1,1,1,1] => 4
[4,3,3,2] => 1
[4,3,3,1,1] => 2
[4,3,2,2,1] => 1
[4,3,2,1,1,1] => 2
[4,3,1,1,1,1,1] => 4
[4,2,2,2,2] => 3
[4,2,2,2,1,1] => 3
[4,2,2,1,1,1,1] => 4
[4,2,1,1,1,1,1,1] => 5
[4,1,1,1,1,1,1,1,1] => 7
[3,3,3,3] => 3
[3,3,3,2,1] => 2
[3,3,3,1,1,1] => 4
[3,3,2,2,2] => 3
[3,3,2,2,1,1] => 3
[3,3,2,1,1,1,1] => 4
[3,3,1,1,1,1,1,1] => 6
[3,2,2,2,2,1] => 3
[3,2,2,2,1,1,1] => 4
[3,2,2,1,1,1,1,1] => 5
[3,2,1,1,1,1,1,1,1] => 6
[3,1,1,1,1,1,1,1,1,1] => 8
[2,2,2,2,2,2] => 5
[2,2,2,2,2,1,1] => 5
[2,2,2,2,1,1,1,1] => 6
[2,2,2,1,1,1,1,1,1] => 7
[2,2,1,1,1,1,1,1,1,1] => 8
[2,1,1,1,1,1,1,1,1,1,1] => 9
[1,1,1,1,1,1,1,1,1,1,1,1] => 11
[5,4,3,1] => 0
[5,4,2,2] => 1
[5,4,2,1,1] => 1
[5,3,3,2] => 1
[5,3,3,1,1] => 2
[5,3,2,2,1] => 1
[4,4,3,2] => 1
[4,4,3,1,1] => 2
[4,4,2,2,1] => 2
[4,3,3,2,1] => 1
[5,4,3,2] => 0
[5,4,3,1,1] => 1
[5,4,2,2,1] => 1
[5,3,3,2,1] => 1
[4,4,3,2,1] => 1
[5,4,3,2,1] => 0
-----------------------------------------------------------------------------
Created: Jan 18, 2018 at 17:35 by Martin Rubey
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Last Updated: Sep 14, 2018 at 19:20 by Martin Rubey