Identifier
Identifier
Values
[1] => 0
[1,1] => 0
[2] => 0
[1,1,1] => 0
[1,2] => 1
[2,1] => -1
[3] => 0
[1,1,1,1] => 0
[1,1,2] => 1
[1,2,1] => 0
[1,3] => 2
[2,1,1] => -1
[2,2] => 0
[3,1] => -2
[4] => 0
[1,1,1,1,1] => 0
[1,1,1,2] => 1
[1,1,2,1] => 0
[1,1,3] => 2
[1,2,1,1] => 0
[1,2,2] => 1
[1,3,1] => 0
[1,4] => 3
[2,1,1,1] => -1
[2,1,2] => 0
[2,2,1] => -1
[2,3] => 1
[3,1,1] => -2
[3,2] => -1
[4,1] => -3
[5] => 0
[1,1,1,1,1,1] => 0
[1,1,1,1,2] => 1
[1,1,1,2,1] => 0
[1,1,1,3] => 2
[1,1,2,1,1] => 0
[1,1,2,2] => 1
[1,1,3,1] => 0
[1,1,4] => 3
[1,2,1,1,1] => 0
[1,2,1,2] => 1
[1,2,2,1] => 0
[1,2,3] => 2
[1,3,1,1] => 0
[1,3,2] => 1
[1,4,1] => 0
[1,5] => 4
[2,1,1,1,1] => -1
[2,1,1,2] => 0
[2,1,2,1] => -1
[2,1,3] => 1
[2,2,1,1] => -1
[2,2,2] => 0
[2,3,1] => -1
[2,4] => 2
[3,1,1,1] => -2
[3,1,2] => -1
[3,2,1] => -2
[3,3] => 0
[4,1,1] => -3
[4,2] => -2
[5,1] => -4
[6] => 0
[1,1,1,1,1,1,1] => 0
[1,1,1,1,1,2] => 1
[1,1,1,1,2,1] => 0
[1,1,1,1,3] => 2
[1,1,1,2,1,1] => 0
[1,1,1,2,2] => 1
[1,1,1,3,1] => 0
[1,1,1,4] => 3
[1,1,2,1,1,1] => 0
[1,1,2,1,2] => 1
[1,1,2,2,1] => 0
[1,1,2,3] => 2
[1,1,3,1,1] => 0
[1,1,3,2] => 1
[1,1,4,1] => 0
[1,1,5] => 4
[1,2,1,1,1,1] => 0
[1,2,1,1,2] => 1
[1,2,1,2,1] => 0
[1,2,1,3] => 2
[1,2,2,1,1] => 0
[1,2,2,2] => 1
[1,2,3,1] => 0
[1,2,4] => 3
[1,3,1,1,1] => 0
[1,3,1,2] => 1
[1,3,2,1] => 0
[1,3,3] => 2
[1,4,1,1] => 0
[1,4,2] => 1
[1,5,1] => 0
[1,6] => 5
[2,1,1,1,1,1] => -1
[2,1,1,1,2] => 0
[2,1,1,2,1] => -1
[2,1,1,3] => 1
[2,1,2,1,1] => -1
[2,1,2,2] => 0
[2,1,3,1] => -1
[2,1,4] => 2
[2,2,1,1,1] => -1
[2,2,1,2] => 0
[2,2,2,1] => -1
[2,2,3] => 1
[2,3,1,1] => -1
[2,3,2] => 0
[2,4,1] => -1
[2,5] => 3
[3,1,1,1,1] => -2
[3,1,1,2] => -1
[3,1,2,1] => -2
[3,1,3] => 0
[3,2,1,1] => -2
[3,2,2] => -1
[3,3,1] => -2
[3,4] => 1
[4,1,1,1] => -3
[4,1,2] => -2
[4,2,1] => -3
[4,3] => -1
[5,1,1] => -4
[5,2] => -3
[6,1] => -5
[7] => 0
click to show generating function       
Description
The variation of a composition.
References
[1] Archibald, M., Knopfmacher, A., Mansour, T. Variation statistics on compositions MathSciNet:2977908
Code
def statistic(alp):
    return sum([alp[i+1]-alp[i] for i in range(len(alp) - 1)])
Created
Jun 13, 2013 at 15:47 by Chris Berg
Updated
Jun 01, 2015 at 16:00 by Martin Rubey