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* www.FindStat.org - The Combinatorial Statistic Finder *
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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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* This information is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
*****************************************************************************
-----------------------------------------------------------------------------
Statistic identifier: St000548
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The number of different non-empty partial sums of an integer partition.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(l):
return len(set(sum(l[i] for i in X) for X in Subsets(range(len(l)))))-1
-----------------------------------------------------------------------------
Statistic values:
[] => 0
[1] => 1
[2] => 1
[1,1] => 2
[3] => 1
[2,1] => 3
[1,1,1] => 3
[4] => 1
[3,1] => 3
[2,2] => 2
[2,1,1] => 4
[1,1,1,1] => 4
[5] => 1
[4,1] => 3
[3,2] => 3
[3,1,1] => 5
[2,2,1] => 5
[2,1,1,1] => 5
[1,1,1,1,1] => 5
[6] => 1
[5,1] => 3
[4,2] => 3
[4,1,1] => 5
[3,3] => 2
[3,2,1] => 6
[3,1,1,1] => 6
[2,2,2] => 3
[2,2,1,1] => 6
[2,1,1,1,1] => 6
[1,1,1,1,1,1] => 6
[7] => 1
[6,1] => 3
[5,2] => 3
[5,1,1] => 5
[4,3] => 3
[4,2,1] => 7
[4,1,1,1] => 7
[3,3,1] => 5
[3,2,2] => 5
[3,2,1,1] => 7
[3,1,1,1,1] => 7
[2,2,2,1] => 7
[2,2,1,1,1] => 7
[2,1,1,1,1,1] => 7
[1,1,1,1,1,1,1] => 7
[8] => 1
[7,1] => 3
[6,2] => 3
[6,1,1] => 5
[5,3] => 3
[5,2,1] => 7
[5,1,1,1] => 7
[4,4] => 2
[4,3,1] => 6
[4,2,2] => 4
[4,2,1,1] => 8
[4,1,1,1,1] => 8
[3,3,2] => 5
[3,3,1,1] => 8
[3,2,2,1] => 8
[3,2,1,1,1] => 8
[3,1,1,1,1,1] => 8
[2,2,2,2] => 4
[2,2,2,1,1] => 8
[2,2,1,1,1,1] => 8
[2,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,1,1] => 8
[9] => 1
[8,1] => 3
[7,2] => 3
[7,1,1] => 5
[6,3] => 3
[6,2,1] => 7
[6,1,1,1] => 7
[5,4] => 3
[5,3,1] => 7
[5,2,2] => 5
[5,2,1,1] => 9
[5,1,1,1,1] => 9
[4,4,1] => 5
[4,3,2] => 7
[4,3,1,1] => 9
[4,2,2,1] => 9
[4,2,1,1,1] => 9
[4,1,1,1,1,1] => 9
[3,3,3] => 3
[3,3,2,1] => 9
[3,3,1,1,1] => 9
[3,2,2,2] => 7
[3,2,2,1,1] => 9
[3,2,1,1,1,1] => 9
[3,1,1,1,1,1,1] => 9
[2,2,2,2,1] => 9
[2,2,2,1,1,1] => 9
[2,2,1,1,1,1,1] => 9
[2,1,1,1,1,1,1,1] => 9
[1,1,1,1,1,1,1,1,1] => 9
[10] => 1
[9,1] => 3
[8,2] => 3
[8,1,1] => 5
[7,3] => 3
[7,2,1] => 7
[7,1,1,1] => 7
[6,4] => 3
[6,3,1] => 7
[6,2,2] => 5
[6,2,1,1] => 9
[6,1,1,1,1] => 9
[5,5] => 2
[5,4,1] => 6
[5,3,2] => 6
[5,3,1,1] => 10
[5,2,2,1] => 10
[5,2,1,1,1] => 10
[5,1,1,1,1,1] => 10
[4,4,2] => 5
[4,4,1,1] => 8
[4,3,3] => 5
[4,3,2,1] => 10
[4,3,1,1,1] => 10
[4,2,2,2] => 5
[4,2,2,1,1] => 10
[4,2,1,1,1,1] => 10
[4,1,1,1,1,1,1] => 10
[3,3,3,1] => 7
[3,3,2,2] => 8
[3,3,2,1,1] => 10
[3,3,1,1,1,1] => 10
[3,2,2,2,1] => 10
[3,2,2,1,1,1] => 10
[3,2,1,1,1,1,1] => 10
[3,1,1,1,1,1,1,1] => 10
[2,2,2,2,2] => 5
[2,2,2,2,1,1] => 10
[2,2,2,1,1,1,1] => 10
[2,2,1,1,1,1,1,1] => 10
[2,1,1,1,1,1,1,1,1] => 10
[1,1,1,1,1,1,1,1,1,1] => 10
[11] => 1
[10,1] => 3
[9,2] => 3
[9,1,1] => 5
[8,3] => 3
[8,2,1] => 7
[8,1,1,1] => 7
[7,4] => 3
[7,3,1] => 7
[7,2,2] => 5
[7,2,1,1] => 9
[7,1,1,1,1] => 9
[6,5] => 3
[6,4,1] => 7
[6,3,2] => 7
[6,3,1,1] => 11
[6,2,2,1] => 11
[6,2,1,1,1] => 11
[6,1,1,1,1,1] => 11
[5,5,1] => 5
[5,4,2] => 7
[5,4,1,1] => 9
[5,3,3] => 5
[5,3,2,1] => 11
[5,3,1,1,1] => 11
[5,2,2,2] => 7
[5,2,2,1,1] => 11
[5,2,1,1,1,1] => 11
[5,1,1,1,1,1,1] => 11
[4,4,3] => 5
[4,4,2,1] => 11
[4,4,1,1,1] => 11
[4,3,3,1] => 9
[4,3,2,2] => 9
[4,3,2,1,1] => 11
[4,3,1,1,1,1] => 11
[4,2,2,2,1] => 11
[4,2,2,1,1,1] => 11
[4,2,1,1,1,1,1] => 11
[4,1,1,1,1,1,1,1] => 11
[3,3,3,2] => 7
[3,3,3,1,1] => 11
[3,3,2,2,1] => 11
[3,3,2,1,1,1] => 11
[3,3,1,1,1,1,1] => 11
[3,2,2,2,2] => 9
[3,2,2,2,1,1] => 11
[3,2,2,1,1,1,1] => 11
[3,2,1,1,1,1,1,1] => 11
[3,1,1,1,1,1,1,1,1] => 11
[2,2,2,2,2,1] => 11
[2,2,2,2,1,1,1] => 11
[2,2,2,1,1,1,1,1] => 11
[2,2,1,1,1,1,1,1,1] => 11
[2,1,1,1,1,1,1,1,1,1] => 11
[1,1,1,1,1,1,1,1,1,1,1] => 11
[12] => 1
[11,1] => 3
[10,2] => 3
[10,1,1] => 5
[9,3] => 3
[9,2,1] => 7
[9,1,1,1] => 7
[8,4] => 3
[8,3,1] => 7
[8,2,2] => 5
[8,2,1,1] => 9
[8,1,1,1,1] => 9
[7,5] => 3
[7,4,1] => 7
[7,3,2] => 7
[7,3,1,1] => 11
[7,2,2,1] => 11
[7,2,1,1,1] => 11
[7,1,1,1,1,1] => 11
[6,6] => 2
[6,5,1] => 6
[6,4,2] => 6
[6,4,1,1] => 10
[6,3,3] => 4
[6,3,2,1] => 12
[6,3,1,1,1] => 12
[6,2,2,2] => 6
[6,2,2,1,1] => 12
[6,2,1,1,1,1] => 12
[6,1,1,1,1,1,1] => 12
[5,5,2] => 5
[5,5,1,1] => 8
[5,4,3] => 7
[5,4,2,1] => 12
[5,4,1,1,1] => 12
[5,3,3,1] => 10
[5,3,2,2] => 9
[5,3,2,1,1] => 12
[5,3,1,1,1,1] => 12
[5,2,2,2,1] => 12
[5,2,2,1,1,1] => 12
[5,2,1,1,1,1,1] => 12
[5,1,1,1,1,1,1,1] => 12
[4,4,4] => 3
[4,4,3,1] => 9
[4,4,2,2] => 6
[4,4,2,1,1] => 12
[4,4,1,1,1,1] => 12
[4,3,3,2] => 10
[4,3,3,1,1] => 12
[4,3,2,2,1] => 12
[4,3,2,1,1,1] => 12
[4,3,1,1,1,1,1] => 12
[4,2,2,2,2] => 6
[4,2,2,2,1,1] => 12
[4,2,2,1,1,1,1] => 12
[4,2,1,1,1,1,1,1] => 12
[4,1,1,1,1,1,1,1,1] => 12
[3,3,3,3] => 4
[3,3,3,2,1] => 12
[3,3,3,1,1,1] => 12
[3,3,2,2,2] => 10
[3,3,2,2,1,1] => 12
[3,3,2,1,1,1,1] => 12
[3,3,1,1,1,1,1,1] => 12
[3,2,2,2,2,1] => 12
[3,2,2,2,1,1,1] => 12
[3,2,2,1,1,1,1,1] => 12
[3,2,1,1,1,1,1,1,1] => 12
[3,1,1,1,1,1,1,1,1,1] => 12
[2,2,2,2,2,2] => 6
[2,2,2,2,2,1,1] => 12
[2,2,2,2,1,1,1,1] => 12
[2,2,2,1,1,1,1,1,1] => 12
[2,2,1,1,1,1,1,1,1,1] => 12
[2,1,1,1,1,1,1,1,1,1,1] => 12
[1,1,1,1,1,1,1,1,1,1,1,1] => 12
[8,5] => 3
[7,5,1] => 7
[7,4,2] => 7
[5,5,3] => 5
[5,4,4] => 5
[5,4,3,1] => 11
[5,4,2,2] => 9
[5,4,2,1,1] => 13
[5,4,1,1,1,1] => 13
[5,3,3,2] => 9
[5,3,3,1,1] => 13
[5,3,2,2,1] => 13
[5,3,2,1,1,1] => 13
[4,4,4,1] => 7
[4,4,3,2] => 11
[4,4,3,1,1] => 13
[4,4,2,2,1] => 13
[4,3,3,3] => 7
[4,3,3,2,1] => 13
[3,3,3,3,1] => 9
[3,3,3,2,2] => 11
[3,3,2,2,2,1] => 13
[9,5] => 3
[8,5,1] => 7
[7,5,2] => 6
[7,4,3] => 6
[6,4,4] => 5
[6,2,2,2,2] => 7
[5,5,4] => 5
[5,5,1,1,1,1] => 14
[5,4,3,2] => 12
[5,4,3,1,1] => 14
[5,4,2,2,1] => 14
[5,4,2,1,1,1] => 14
[5,3,3,2,1] => 14
[5,3,2,2,2] => 12
[5,2,2,2,2,1] => 14
[4,4,4,2] => 7
[4,4,3,3] => 8
[4,4,3,2,1] => 14
[4,3,2,2,2,1] => 14
[3,3,3,3,2] => 9
[3,3,3,3,1,1] => 14
[9,5,1] => 7
[8,5,2] => 7
[7,5,3] => 7
[6,5,4] => 7
[6,5,1,1,1,1] => 15
[6,3,3,3] => 5
[6,2,2,2,2,1] => 15
[5,5,5] => 3
[5,4,3,2,1] => 15
[5,4,3,1,1,1] => 15
[5,3,2,2,2,1] => 15
[4,4,4,3] => 7
[4,4,4,1,1,1] => 15
[3,3,3,3,3] => 5
[3,3,3,3,2,1] => 15
[8,5,3] => 6
[7,5,3,1] => 14
[5,5,3,3] => 8
[5,5,2,2,2] => 11
[5,4,3,2,1,1] => 16
[5,4,2,2,2,1] => 16
[4,4,4,4] => 4
[4,4,4,2,2] => 8
[4,3,3,3,2,1] => 16
[8,6,3] => 7
[6,5,3,3] => 9
[6,5,2,2,2] => 13
[6,4,4,3] => 11
[6,4,4,1,1,1] => 17
[6,3,3,3,2] => 11
[6,3,3,3,1,1] => 17
[5,5,4,3] => 11
[5,5,4,1,1,1] => 17
[5,5,2,2,2,1] => 17
[5,4,3,2,2,1] => 17
[5,3,3,3,2,1] => 17
[4,4,4,3,2] => 15
[4,4,4,3,1,1] => 17
[4,4,4,2,2,1] => 17
[4,4,4,3,2,1] => 18
[5,4,3,3,2,1] => 18
[6,3,3,3,2,1] => 18
[6,5,2,2,2,1] => 18
[5,5,3,3,1,1] => 18
[6,5,4,1,1,1] => 18
[5,5,3,3,2] => 13
[5,5,4,2,2] => 14
[6,4,4,2,2] => 9
[6,5,4,3] => 14
[9,6,3] => 6
[8,6,4] => 7
[5,4,4,3,2,1] => 19
[5,5,3,3,2,1] => 19
[5,5,4,2,2,1] => 19
[6,4,4,2,2,1] => 19
[5,5,4,3,1,1] => 19
[6,4,4,3,1,1] => 19
[6,5,3,3,1,1] => 19
[5,5,4,3,2] => 17
[6,4,4,3,2] => 17
[6,5,3,3,2] => 15
[6,5,4,2,2] => 15
[6,5,4,3,1] => 17
[6,5,4,1,1,1,1] => 19
[9,6,4] => 7
[8,5,4,2] => 15
[8,5,5,1] => 11
[5,5,4,3,2,1] => 20
[6,4,4,3,2,1] => 20
[6,5,3,3,2,1] => 20
[6,5,4,2,2,1] => 20
[6,5,4,3,1,1] => 20
[6,5,4,3,2] => 18
[6,5,2,2,2,2,1] => 20
[6,5,4,2,1,1,1] => 20
[7,5,4,3,1] => 18
[8,6,4,2] => 10
[10,6,4] => 6
[10,7,3] => 6
[9,7,4] => 7
[9,5,5,1] => 10
[6,5,4,3,2,1] => 21
[6,3,3,3,3,2,1] => 21
[6,5,3,2,2,2,1] => 21
[6,5,4,3,1,1,1] => 21
[11,7,3] => 7
[4,4,4,4,3,2,1] => 22
[6,4,3,3,3,2,1] => 22
[6,5,4,2,2,2,1] => 22
[6,5,4,3,2,1,1] => 22
[9,6,4,3] => 13
[5,4,4,4,3,2,1] => 23
[6,5,3,3,3,2,1] => 23
[6,5,4,3,2,2,1] => 23
[9,6,5,3] => 13
[8,6,5,3,1] => 21
[6,4,4,4,3,2,1] => 24
[6,5,4,3,3,2,1] => 24
[11,7,5,1] => 14
[9,7,5,3] => 14
[5,5,5,4,3,2,1] => 25
[6,5,4,4,3,2,1] => 25
[9,7,5,3,1] => 23
[10,7,5,3] => 13
[6,5,5,4,3,2,1] => 26
[9,7,5,4,1] => 22
[6,6,5,4,3,2,1] => 27
[7,6,5,4,3,2] => 25
[7,6,5,4,3,2,1] => 28
[7,6,5,4,3,1,1,1] => 28
[10,7,6,4,1] => 22
[9,7,6,4,2] => 21
[10,8,5,4,1] => 22
[7,6,5,4,3,2,1,1] => 29
[7,6,5,4,2,2,2,1] => 29
[10,8,6,4,1] => 25
[9,7,5,5,3,1] => 28
[7,6,5,4,3,2,2,1] => 30
[7,6,5,3,3,3,2,1] => 30
[11,8,6,4,1] => 26
[10,8,6,4,2] => 15
[7,6,5,4,3,3,2,1] => 31
[7,6,4,4,4,3,2,1] => 31
[11,8,6,5,1] => 23
[7,6,5,4,4,3,2,1] => 32
[7,5,5,5,4,3,2,1] => 32
[7,6,5,5,4,3,2,1] => 33
[6,6,6,5,4,3,2,1] => 33
[7,6,6,5,4,3,2,1] => 34
[12,9,7,5,1] => 26
[7,7,6,5,4,3,2,1] => 35
[13,9,7,5,1] => 27
[11,9,7,5,3,1] => 34
[11,8,7,5,4,1] => 32
[8,7,6,5,4,3,2,1] => 36
[8,7,6,5,4,3,2,1,1] => 37
[8,7,6,5,4,3,2,2,1] => 38
[8,7,6,5,4,3,3,2,1] => 39
[8,7,6,5,4,4,3,2,1] => 40
[11,9,7,5,5,3] => 32
[8,7,6,5,5,4,3,2,1] => 41
[8,7,6,6,5,4,3,2,1] => 42
[8,7,7,6,5,4,3,2,1] => 43
[8,8,7,6,5,4,3,2,1] => 44
[9,8,7,6,5,4,3,2,1] => 45
[11,9,7,7,5,3,3] => 39
[11,9,7,6,5,3,1] => 40
[13,11,9,7,5,3,1] => 47
[13,11,9,7,7,5,3,1] => 54
[17,13,11,9,7,5,1] => 57
[15,13,11,9,7,5,3,1] => 62
[29,23,19,17,13,11,7,1] => 98
-----------------------------------------------------------------------------
Created: Jul 16, 2016 at 16:39 by Christian Stump
-----------------------------------------------------------------------------
Last Updated: Jun 17, 2021 at 10:53 by Martin Rubey