- FindStat

Identifier

St000091: Integer compositions ⟶ ℤ

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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Description

The descent variation of a composition.
Defined in [1].

References

[1] Archibald, M., Knopfmacher, A., Mansour, T. Variation statistics on compositions MathSciNet:2977908

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]])

Created

Jun 13, 2013 at 15:53 by Chris Berg

Updated

May 29, 2015 at 16:46 by Martin Rubey