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Statistic identifier: St000225
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Collection: Integer partitions
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Description: Difference between largest and smallest parts in a partition.
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References: [1] Andrews, G. E., Beck, M., Robbins, N. Partitions with fixed differences between largest and smallest parts [[arXiv:1406.3374]]
[2] Triangle read by rows, 0<=k<n: T(n,k) = number of partitions of n such that the differences between greatest and smallest parts are k. [[OEIS:A097364]]
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Code:
def statistic(L):
return L[0]-L[-1]
-----------------------------------------------------------------------------
Statistic values:
[1] => 0
[2] => 0
[1,1] => 0
[3] => 0
[2,1] => 1
[1,1,1] => 0
[4] => 0
[3,1] => 2
[2,2] => 0
[2,1,1] => 1
[1,1,1,1] => 0
[5] => 0
[4,1] => 3
[3,2] => 1
[3,1,1] => 2
[2,2,1] => 1
[2,1,1,1] => 1
[1,1,1,1,1] => 0
[6] => 0
[5,1] => 4
[4,2] => 2
[4,1,1] => 3
[3,3] => 0
[3,2,1] => 2
[3,1,1,1] => 2
[2,2,2] => 0
[2,2,1,1] => 1
[2,1,1,1,1] => 1
[1,1,1,1,1,1] => 0
[7] => 0
[6,1] => 5
[5,2] => 3
[5,1,1] => 4
[4,3] => 1
[4,2,1] => 3
[4,1,1,1] => 3
[3,3,1] => 2
[3,2,2] => 1
[3,2,1,1] => 2
[3,1,1,1,1] => 2
[2,2,2,1] => 1
[2,2,1,1,1] => 1
[2,1,1,1,1,1] => 1
[1,1,1,1,1,1,1] => 0
[8] => 0
[7,1] => 6
[6,2] => 4
[6,1,1] => 5
[5,3] => 2
[5,2,1] => 4
[5,1,1,1] => 4
[4,4] => 0
[4,3,1] => 3
[4,2,2] => 2
[4,2,1,1] => 3
[4,1,1,1,1] => 3
[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] => 2
[2,2,2,2] => 0
[2,2,2,1,1] => 1
[2,2,1,1,1,1] => 1
[2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1] => 0
[9] => 0
[8,1] => 7
[7,2] => 5
[7,1,1] => 6
[6,3] => 3
[6,2,1] => 5
[6,1,1,1] => 5
[5,4] => 1
[5,3,1] => 4
[5,2,2] => 3
[5,2,1,1] => 4
[5,1,1,1,1] => 4
[4,4,1] => 3
[4,3,2] => 2
[4,3,1,1] => 3
[4,2,2,1] => 3
[4,2,1,1,1] => 3
[4,1,1,1,1,1] => 3
[3,3,3] => 0
[3,3,2,1] => 2
[3,3,1,1,1] => 2
[3,2,2,2] => 1
[3,2,2,1,1] => 2
[3,2,1,1,1,1] => 2
[3,1,1,1,1,1,1] => 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
[1,1,1,1,1,1,1,1,1] => 0
[10] => 0
[9,1] => 8
[8,2] => 6
[8,1,1] => 7
[7,3] => 4
[7,2,1] => 6
[7,1,1,1] => 6
[6,4] => 2
[6,3,1] => 5
[6,2,2] => 4
[6,2,1,1] => 5
[6,1,1,1,1] => 5
[5,5] => 0
[5,4,1] => 4
[5,3,2] => 3
[5,3,1,1] => 4
[5,2,2,1] => 4
[5,2,1,1,1] => 4
[5,1,1,1,1,1] => 4
[4,4,2] => 2
[4,4,1,1] => 3
[4,3,3] => 1
[4,3,2,1] => 3
[4,3,1,1,1] => 3
[4,2,2,2] => 2
[4,2,2,1,1] => 3
[4,2,1,1,1,1] => 3
[4,1,1,1,1,1,1] => 3
[3,3,3,1] => 2
[3,3,2,2] => 1
[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] => 2
[3,1,1,1,1,1,1,1] => 2
[2,2,2,2,2] => 0
[2,2,2,2,1,1] => 1
[2,2,2,1,1,1,1] => 1
[2,2,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1] => 0
[5,4,2] => 3
[5,4,1,1] => 4
[5,3,3] => 2
[5,3,2,1] => 4
[5,3,1,1,1] => 4
[5,2,2,2] => 3
[5,2,2,1,1] => 4
[4,4,3] => 1
[4,4,2,1] => 3
[4,4,1,1,1] => 3
[4,3,3,1] => 3
[4,3,2,2] => 2
[4,3,2,1,1] => 3
[4,2,2,2,1] => 3
[3,3,3,2] => 1
[3,3,3,1,1] => 2
[3,3,2,2,1] => 2
[6,4,2] => 4
[5,4,3] => 2
[5,4,2,1] => 4
[5,4,1,1,1] => 4
[5,3,3,1] => 4
[5,3,2,2] => 3
[5,3,2,1,1] => 4
[5,2,2,2,1] => 4
[4,4,3,1] => 3
[4,4,2,2] => 2
[4,4,2,1,1] => 3
[4,3,3,2] => 2
[4,3,3,1,1] => 3
[4,3,2,2,1] => 3
[3,3,3,2,1] => 2
[3,3,2,2,1,1] => 2
[5,4,3,1] => 4
[5,4,2,2] => 3
[5,4,2,1,1] => 4
[5,3,3,2] => 3
[5,3,3,1,1] => 4
[5,3,2,2,1] => 4
[4,4,3,2] => 2
[4,4,3,1,1] => 3
[4,4,2,2,1] => 3
[4,3,3,2,1] => 3
[5,4,3,2] => 3
[5,4,3,1,1] => 4
[5,4,2,2,1] => 4
[5,3,3,2,1] => 4
[4,4,3,2,1] => 3
[5,4,3,2,1] => 4
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Created: Oct 13, 2014 at 14:17 by Matthias Beck
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Last Updated: Jun 05, 2020 at 14:05 by Martin Rubey