AscentVariation on IntegerComposition
The sum of c(i+1) - c(i) over the positions where it is positive.
Archibald, Knopfmacher and Mansour, Variation statistics on compositions. FindStat titles it the descent variation; it sums the rises, which is equidistributed with the sum of the falls under reversal.
Called as CombinatorialStat(x, "AscentVariation"). The head's page has its examples.
Live
Distribution
Over IntegerCompositions at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St000091
The descent variation of a composition.
| Object | Value |
|---|---|
[1] | 0 |
[2] | 0 |
[3] | 0 |
[4] | 0 |
[5] | 0 |
[6] | 0 |
[7] | 0 |
[1,1] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000091 has the rest.