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Statistic identifier: St000091
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Collection: Integer compositions
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Description: The descent variation of a composition.
Defined in [1].
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References: [1] Archibald, M., Knopfmacher, A., Mansour, T. Variation statistics on compositions [[MathSciNet:2977908]]
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Code:
def statistic(alp):
return sum([abs(alp[i+1]-alp[i]) for i in range(len(alp) - 1) if alp[i+1] > alp[i]])
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Statistic values:
[1] => 0
[1,1] => 0
[2] => 0
[1,1,1] => 0
[1,2] => 1
[2,1] => 0
[3] => 0
[1,1,1,1] => 0
[1,1,2] => 1
[1,2,1] => 1
[1,3] => 2
[2,1,1] => 0
[2,2] => 0
[3,1] => 0
[4] => 0
[1,1,1,1,1] => 0
[1,1,1,2] => 1
[1,1,2,1] => 1
[1,1,3] => 2
[1,2,1,1] => 1
[1,2,2] => 1
[1,3,1] => 2
[1,4] => 3
[2,1,1,1] => 0
[2,1,2] => 1
[2,2,1] => 0
[2,3] => 1
[3,1,1] => 0
[3,2] => 0
[4,1] => 0
[5] => 0
[1,1,1,1,1,1] => 0
[1,1,1,1,2] => 1
[1,1,1,2,1] => 1
[1,1,1,3] => 2
[1,1,2,1,1] => 1
[1,1,2,2] => 1
[1,1,3,1] => 2
[1,1,4] => 3
[1,2,1,1,1] => 1
[1,2,1,2] => 2
[1,2,2,1] => 1
[1,2,3] => 2
[1,3,1,1] => 2
[1,3,2] => 2
[1,4,1] => 3
[1,5] => 4
[2,1,1,1,1] => 0
[2,1,1,2] => 1
[2,1,2,1] => 1
[2,1,3] => 2
[2,2,1,1] => 0
[2,2,2] => 0
[2,3,1] => 1
[2,4] => 2
[3,1,1,1] => 0
[3,1,2] => 1
[3,2,1] => 0
[3,3] => 0
[4,1,1] => 0
[4,2] => 0
[5,1] => 0
[6] => 0
[1,1,1,1,1,1,1] => 0
[1,1,1,1,1,2] => 1
[1,1,1,1,2,1] => 1
[1,1,1,1,3] => 2
[1,1,1,2,1,1] => 1
[1,1,1,2,2] => 1
[1,1,1,3,1] => 2
[1,1,1,4] => 3
[1,1,2,1,1,1] => 1
[1,1,2,1,2] => 2
[1,1,2,2,1] => 1
[1,1,2,3] => 2
[1,1,3,1,1] => 2
[1,1,3,2] => 2
[1,1,4,1] => 3
[1,1,5] => 4
[1,2,1,1,1,1] => 1
[1,2,1,1,2] => 2
[1,2,1,2,1] => 2
[1,2,1,3] => 3
[1,2,2,1,1] => 1
[1,2,2,2] => 1
[1,2,3,1] => 2
[1,2,4] => 3
[1,3,1,1,1] => 2
[1,3,1,2] => 3
[1,3,2,1] => 2
[1,3,3] => 2
[1,4,1,1] => 3
[1,4,2] => 3
[1,5,1] => 4
[1,6] => 5
[2,1,1,1,1,1] => 0
[2,1,1,1,2] => 1
[2,1,1,2,1] => 1
[2,1,1,3] => 2
[2,1,2,1,1] => 1
[2,1,2,2] => 1
[2,1,3,1] => 2
[2,1,4] => 3
[2,2,1,1,1] => 0
[2,2,1,2] => 1
[2,2,2,1] => 0
[2,2,3] => 1
[2,3,1,1] => 1
[2,3,2] => 1
[2,4,1] => 2
[2,5] => 3
[3,1,1,1,1] => 0
[3,1,1,2] => 1
[3,1,2,1] => 1
[3,1,3] => 2
[3,2,1,1] => 0
[3,2,2] => 0
[3,3,1] => 0
[3,4] => 1
[4,1,1,1] => 0
[4,1,2] => 1
[4,2,1] => 0
[4,3] => 0
[5,1,1] => 0
[5,2] => 0
[6,1] => 0
[7] => 0
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Created: Jun 13, 2013 at 15:53 by Chris Berg
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Last Updated: May 29, 2015 at 16:46 by Martin Rubey