BargraphValleyHeightSum on IntegerComposition
The sum of the heights of the valleys of the bargraph.
A valley is a fall, level steps, then a rise (Deutsch and Elizalde, A bijection between bargraphs and Dyck paths).
Called as CombinatorialStat(x, "BargraphValleyHeightSum"). 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 St000807
The sum of the heights of the valleys of the associated bargraph.
| Object | Value |
|---|---|
[1] | 0 |
[2] | 0 |
[3] | 0 |
[4] | 0 |
[5] | 0 |
[6] | 0 |
[7] | 0 |
[8] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000807 has the rest.